📄 Read the survey · 📚 Browse 346 papers · 🗺️ Compare core systems · 📝 Cite

A curated list of continuous-space diffusion and flow language models: models that generate text by iteratively refining real-valued representations (or by one-step maps distilled from such processes), then decoding them into tokens.
This is the companion repository of our survey Continuous-Space Diffusion and Flow Language Models: A Survey, and the list follows the survey's structure.

📢 News

• [2026-10] 🎉 Our survey Continuous-Space Diffusion and Flow Language Models: A Survey is out (PDF), together with this paper list, which tracks literature through 24 October 2026. The arXiv version is coming soon.

📖 About the Survey

Continuous-Space Diffusion and Flow Language Models: A Survey TokenRhythm Technologies October 2026 · 133 pages · literature through 24 October 2026 📄 PDF · arXiv (coming soon) · 📝 BibTeX · 🗺️ Core-system lookup The survey organizes continuous-space text generation by state, transition, and text interface, compares published evidence on sample quality, likelihood, controllability, and end-to-end latency, and closes with open problems in likelihood scaling, readout fidelity, few-step serving, representation reuse, and post-training. Use this list to browse the literature, and the core-system lookup to compare method configurations.

Contents

• 🧭 The Survey at a Glance
• 📚 Surveys and Tutorials (7)
• 🧱 Foundations (15)
• 🧩 The State: Text Representations (76)
  • Token Embeddings (11)
  • Vocabulary, Simplex, Spherical, and Bit States (21)
  • Contextual Encodings (12)
  • Compressed Latent Codes (13)
  • Sentence and Segment Vectors (8)
  • Hybrid Continuous–Discrete States (Boundary) (11)
• ⚙️ The Transition: Learning the Denoiser (36)
  • Prediction Targets and Objectives (13)
  • Training Stages and Module Adaptation (7)
  • Noise Schedules and Self-Conditioning (16)
• 🚀 Sampling, the Text Interface, and Generation Order (64)
  • Samplers and Few-Step Generation (37)
  • From States to Tokens (6)
  • Generation Order and Length (11)
  • Conditioning and Guidance (10)
• 🎯 Tasks and Applications (135)
  • Controllable Generation and Editing (22)
  • Sequence-to-Sequence Generation (15)
  • Captioning and Multimodal Generation (51)
  • Dialogue and Discourse Planning (7)
  • Code, Structured Outputs, and Synthetic Data (10)
  • Reasoning, Knowledge, and Instruction Following (23)
  • Scientific and Domain Applications (7)
• 📊 Evaluation, Analysis, and Theory (13)
• 🗺️ Core Systems at a Glance
• 🔗 Related Awesome Lists
• 📝 Citation

Tip

Reading the tables. Papers are sorted newest first within each section. Date is the arXiv announcement month (taken from the identifier) when an arXiv version exists, otherwise the publication month. ◆ marks the 133 core systems indexed in the survey's lookup table and jumps to that system in Core Systems at a Glance. Star badges link to the official code.

🧭 The Survey at a Glance

The survey organizes the literature around three coupled design dimensions:

• 🟦 State — what does a position hold? Token embeddings, simplex coordinates, and contextual, compressed, or sentence-level representations (§3).
• 🟩 Transition — how is the state revised? Training objectives, noise schedules, solvers, and generation order (§4–§5).
• 🟧 Text interface — where do words enter? Direct vocabulary readout, or a separate parallel or autoregressive decoder (§5).

Key findings

1. Recurring failure modes. Squared-error regression causes rounding ambiguity and embedding collapse. Noise schedules inherited from images are uninformative. Learned priors mismatch the latents of clean-text autoencoders. Few-step samplers average over modes.
2. Sample-quality parity, but a likelihood gap. Continuous models can match same-scale autoregressive sample quality on prompt continuation, but they still lag in held-out likelihood bounds and require substantially more training compute under current scaling laws, even as the self-conditioned RePlaid matches or improves on discrete masked diffusion in held-out likelihood bounds past compute-optimal budgets.
3. Where they win today. The clearest gains are in gradient-guided structural control, plan-level diversity, image-to-text flow captioning, and task-specific reasoning after targeted fine-tuning.
4. Few-step generation. Naive coarse solvers and several undistilled one-step flow maps collapse in entropy; trajectory-consistent distillation and stochastic bridges prevent this.
5. Latency. Standalone continuous generators have not yet surpassed optimized autoregressive baselines in end-to-end latency at matched quality. The matched-quality wall-clock speedups reported to date rely on autoregressive verification of continuous drafts.

Timeline

_{Representative systems and studies ordered by first public posting, colored by the state family they refine; boxes in gray italics are discrete-diffusion reference points. † marks one- or few-step flow-map, distillation, or drifting methods, and bold names mark systems with 7B or more parameters. The axis is not to scale: 2026 is split into January–March, April–May, June–August, September, and October, the months in which most recent work appeared. Click the figure for full resolution.}

Taxonomy of core systems (state → transition and order → decoder)

How this list maps to the survey

Survey section	What it covers	In this list
§2 Background	Diffusion and flow matching, recurring failure modes, the boundary with discrete diffusion	Foundations
§3 The State	Token embeddings, simplex, spherical, and bit states, contextual encodings, compressed codes, sentence vectors	The State
§4 The Transition	Prediction targets, training stages and module adaptation, noise schedules, and self-conditioning	The Transition
§5 Sampling, the Text Interface, and Generation Order	Few-step samplers, readout and decoders, generation order, guidance	Sampling, Text Interface, and Order
§6 Tasks, Evidence, and Evaluation	Six capability reviews, evaluation measures, cross-paper empirical comparisons	Tasks · Evaluation
§7 Open Problems	Likelihood and compute gap, precise text recovery, few-step latency, length, interpretability and optimization	Evaluation, Analysis, and Theory
App. F–G	Method lookup table and extended catalog of systems	Core systems at a glance · Tasks

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📚 Surveys and Tutorials

Surveys, tutorials, and expert syntheses that cover continuous text diffusion. Table 1 of our survey compares how each one organizes continuous models. _{(Survey §1.2)}

Model	Paper	Venue	Date	Code
The Latent Space	The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook Examines latent-space computation in language-based models, organizing reasoning, planning, and memory work by mechanism and capability across Foundation, Evolution, Mechanism, Ability, and Outlook perspectives.	arXiv	2026.04
—	Continuous diffusion language models Synthesizes in a blog post the case for revisiting continuous diffusion language models, covering embeddings, losses, schedules, self-conditioning, and distillability.	Blog	2026	—
—	A Survey on Diffusion Language Models Traces the diffusion language model landscape, centering on discrete diffusion while devoting one chronological section to continuous models from Diffusion-LM to ELF, Cola, and BitLM.	arXiv	2025.08
—	Discrete Diffusion in Large Language and Multimodal Models: A Survey Restricts its survey to discrete diffusion large language and multimodal models, reviewing their parallel multi-token decoding with full attention and denoising-based generation.	TMLR 2026	2025.06
—	Diffusion models in text generation: a survey Organizes diffusion models for text generation by downstream task, covering conditional generation, unconstrained generation, and fine-grained control.	PeerJ Computer Science 2024	2024	—
—	A Survey of Diffusion Models in Natural Language Processing Reviews diffusion models across natural language processing, contrasting discrete and continuous formulations, comparing them with autoregressive models, and cataloging applications.	arXiv	2023.05	—
—	Diffusion Models for Non-autoregressive Text Generation: A Survey Surveys diffusion models for non-autoregressive text generation, separating discrete from continuous formulations and reviewing diffusion-process design and pretrained language model integration.	IJCAI 2023	2023.03

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🧱 Diffusion and Flow Foundations

The continuous generative-modeling toolkit the field builds on: denoising diffusion, score SDEs and fast solvers, flow matching and stochastic interpolants, flow maps and consistency models, distillation, and guidance. _{(Survey §2.2)}

Model	Paper	Venue	Date	Code
MeanFlow	Mean Flows for One-step Generative Modeling Models the average velocity over an interval through its Eulerian identity with the instantaneous velocity for one-step generation, a parameterization DiLaDiff adopts to distill latent text velocities.	NeurIPS 2025	2025.05
Flow Map Matching	Flow Map Matching with Stochastic Interpolants: A Mathematical Framework for Consistency Models Frames consistency models as learning the two-time flow map of a stochastic-interpolant model, by distillation or direct training, with an average velocity obeying a Lagrangian identity.	TMLR 2025	2024.06	—
Dirichlet FM	Dirichlet Flow Matching with Applications to DNA Sequence Design Transports points on the probability simplex toward vertices along Dirichlet paths with posterior-weighted conditional fields, demonstrated on DNA sequence design and reused as simplex-path geometry by text models.	ICML 2024	2024.02
DMD	One-step Diffusion with Distribution Matching Distillation Matches a one- or few-step student to a diffusion teacher in distribution at every noise level using score differences, a distillation family DLM-One instantiates for continuous text.	CVPR 2024	2023.11	—
Stochastic Interpolants	Stochastic Interpolants: A Unifying Framework for Flows and Diffusions Unifies flows and diffusions by bridging two densities with a stochastic interpolant path plus an optional latent noise term, covering both deterministic and stochastic generative models.	JMLR 2025	2023.03	—
Consistency Models	Consistency Models Maps every point along one trajectory to the same endpoint, the endpoint case of a flow map, enabling one-step generation via distillation or standalone training.	ICML 2023	2023.03
DPM-Solver++	DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models Solves the diffusion ODE by integrating its linear part exactly in log signal-to-noise ratio and approximating the clean-state prediction with a low-order polynomial, reducing to DDIM at first order.	Mach. Intell. Res. 2025	2022.11
Flow Matching	Flow Matching for Generative Modeling Regresses velocity fields of fixed conditional probability paths to train continuous normalizing flows simulation-free, with the same parameter gradient as regression on the marginal velocity.	ICLR 2023	2022.10
Rectified Flow	Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow Performs flow matching with the linear interpolant and adds a reflow step that re-pairs noise and data along the learned coupling to straighten trajectories.	ICLR 2023	2022.09
CFG	Classifier-Free Diffusion Guidance Guides diffusion sampling without an external classifier by training with the condition randomly dropped and extrapolating conditional and unconditional estimates.	arXiv	2022.07	—
Progressive Distillation	Progressive Distillation for Fast Sampling of Diffusion Models Distills a many-step deterministic diffusion sampler by repeatedly halving its step count, and introduces the v-parameterization that avoids dividing by a vanishing signal coefficient.	ICLR 2022	2022.02	—
LDM	High-Resolution Image Synthesis with Latent Diffusion Models Moves image diffusion into the latent space of a pretrained autoencoder, supplying the encoder–generator–decoder decomposition that latent text codec systems later borrow.	CVPR 2022	2021.12
Score SDE	Score-Based Generative Modeling through Stochastic Differential Equations Reverses a noise-injecting SDE using the learned time-dependent score and derives a probability-flow ODE that shares every time-marginal with the reverse-time SDE.	ICLR 2021	2020.11
DDIM	Denoising Diffusion Implicit Models Replaces the Markovian forward process of DDPM with non-Markovian ones sharing its training objective, giving a deterministic sampler that re-forms each state from the predicted clean state and noise.	ICLR 2021	2020.10
DDPM	Denoising Diffusion Probabilistic Models Introduces denoising diffusion probabilistic models trained on a weighted variational bound, sampling ancestrally from the Gaussian forward posterior evaluated at the predicted clean state.	NeurIPS 2020	2020.06

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🧩 The State: Text Representations

What does one position hold? Systems grouped by the real-valued object the sampler refines. _{(Survey §3)}

Token Embeddings

One vector per token, looked up from a learned or frozen embedding table. Learned tables need explicit token-identity anchoring to avoid embedding collapse. _{(Survey §3.1)}

Model	Paper	Venue	Date	Code
LLaCO ◆	LLaCO: Continuous Diffusion for Large Language Models with Competition-Aware Semantic Scheduling Adapts Nemotron-Labs-Diffusion-8B to great-circle diffusion over frozen unit embedding directions, warping time by the source token's log-rank degradation, which substantially outperforms top-1 or linear-rank schedules on mathematical reasoning.	arXiv	2026.10
S-FLM ◆	Language Modeling with Hyperspherical Flows Normalizes learned token embeddings onto a hypersphere and transports spherical noise along a tangent velocity field, deriving its schedule truncation from a spherical random-embedding model.	TMLR 2026	2026.05
DSL ◆	Discrete Stochastic Localization for Non-autoregressive Generation Formulates stochastic localization on unit-sphere token embeddings with an SNR-invariant Bayes-optimal denoiser, and fine-tunes an MDLM checkpoint that then supports continuous, random-order, and hybrid continuous-then-discrete sampling.	NeurIPS 2026	2026.02	—
—	Understanding Encoding in Continuous Diffusion Language Models Shows that a continuous diffusion language model's encoding defines the continuous target distribution, so its vector dimension, geometry, and compatibility with the denoiser's input and output parameterizations affect sample quality.	ICLR 2027 submission	2026	—
LanGeo	Geometry-aware Euclidean Diffusion Language Generation Develops geometry-aware Euclidean diffusion for language generation, an alternative token-level state parameterization based on normalized-embedding mixtures.	OpenReview	2025	—
Boundary-Conditional Diffusion ◆	Discrete Modeling via Boundary Conditional Diffusion Processes Constructs a two-step forward process that first estimates the discrete boundary as a prior and then rescales the embedding diffusion trajectory, with machine translation and summarization experiments.	NeurIPS 2024	2024.10	—
Plaid ◆	Likelihood-Based Diffusion Language Models Learns embeddings inside a variational likelihood bound anchored by an endpoint token cross-entropy, making continuous models directly comparable with autoregressive ones in held-out bits per byte.	NeurIPS 2023	2023.05
SED ◆	Self-conditioned Embedding Diffusion for Text Generation Freezes a low-dimensional token-embedding table from a bottleneck-trained BERT to rule out embedding collapse, then runs self-conditioned Gaussian diffusion with squared-error denoising and a stop-gradient readout head.	arXiv	2022.11	—
CDCD ◆	Continuous diffusion for categorical data Diffuses L2-normalized learned embeddings under token-posterior cross-entropy and time warping, matching a 1.3B autoregressive baseline on C4 prompt completion with MAUVE 0.953 versus 0.940.	arXiv	2022.11	—
DiffuSeq ◆	DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models Concatenates source and target token embeddings and corrupts only the target, keeping the clean source visible at every update for paraphrase, question generation, dialogue, and simplification.	ICLR 2023	2022.10
Diffusion-LM ◆	Diffusion-LM Improves Controllable Text Generation Denoises Gaussian vectors into learned word embeddings with a rounding term and nearest-embedding clamping, and steers the differentiable state with classifier gradients for syntactic and attribute control.	NeurIPS 2022	2022.05

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Vocabulary, Simplex, Spherical, and Bit States

Vocabulary-sized logits, simplex points, and categorical beliefs; spherical and probability-geometry states; analog bit codes and rendered glyphs. _{(Survey §3.1)}

Model	Paper	Venue	Date	Code
H-CoBit ◆	Denoising Hierarchical Representations: Joint Continuous Diffusion for Language Modeling Appends bits naming k-means clusters of pretrained token embeddings to CoBit's analog token bits and co-denoises both channels under per-channel schedules, improving generative perplexity at dataset entropy and MAUVE at or above it, while a matched random-cluster ablation removes the perplexity advantage.	arXiv	2026.10
SDM ◆	Simplex Diffusion Models Corrupts simplex states by Dirichlet diffusion with closed-form reverse bridges and churn-controlled sampling, outperforming self-conditioned masked diffusion and a reimplemented Dirichlet Flow Matching baseline on GSM8K code generation after TinyGSM training while trailing a greedy autoregressive baseline.	arXiv	2026.09	—
CoBit ◆	Towards Closing the Autoregressive Gap in Language Modeling via Entropy-Gated Continuous Bitstream Diffusion Runs continuous diffusion over fixed-width analog bitstreams that encode tokens, using a matched-filter residual parameterization and Langevin-type sampling corrections gated by the entropy-rate profile.	NeurIPS 2026	2026.05
—	Spherical Flows for Sampling Categorical Data Keeps token-aligned states on the sphere under von Mises-Fisher noise, computing velocities from a learned token posterior and reaching its best results with predictor–corrector sampling and entropy-constrained selection.	NeurIPS 2026	2026.05	—
BitLM ◆	BitLM: Unlocking Multi-Token Language Generation with Bitwise Continuous Diffusion Encodes each token as a fixed-length binary code and uses a lightweight diffusion head to denoise multiple tokens per block in parallel, keeping causal attention across blocks.	arXiv	2026.05	—
—	Spherical Brownian Diffusion for Language Modeling Proposes Brownian motion on the sphere as the forward process for spherical token states, whose heat semigroup supplies a dimension-free additive noise clock and an analytic ancestral bridge.	arXiv	2026	—
SimpLM	SimpLM: Simplex-Based Flow Language Modeling via Autoregressive Adaptation Converts a pretrained autoregressive model into a flow language model whose per-position state lies on the vocabulary simplex.	COLM 2026 Workshop	2026	—
—	Inside the Scaling of Riemannian Flow Language Models: Geometry, Generation, and Conditioning Studies how hyperspherical Riemannian flow language models (SwaFlow, up to 3.741B parameters including embeddings) scale, analyzing token-embedding geometry, unconditional generation, and conditioning, including the effect of adding clean-prefix examples late in training.	ICLR 2027 submission	2026	—
—	Simplex-to-Euclidean Bijections for Categorical Flow Matching Transforms the open simplex into Euclidean space with smooth Aitchison-geometry bijections for categorical flow matching, dequantizing discrete data by Dirichlet interpolation with exact recovery of the original distribution.	AISTATS 2026	2025.10	—
Smoothie ◆	Smoothie: Smoothing Diffusion on Token Embeddings for Text Generation Represents each position by a vocabulary-sized distance vector corrupted by Gaussian noise, converting MSE-trained clean-embedding predictions back into distance coordinates during reverse updates and ending with an argmax readout.	ICML 2026	2025.05
—	Riemannian Flow Matching on the Fisher–Rao Sphere for Non-Autoregressive Conditional Text Generation Applies Riemannian flow matching on the Fisher–Rao sphere to non-autoregressive conditional text generation, adding a token cross-entropy on a one-update reconstruction to tie geometry to lexical recovery.	ARR submission	2025.05	—
α-Flow	α-Flow: A Unified Framework for Continuous-State Discrete Flow Matching Models Casts continuous-state discrete flow matching as flows on α-representations of categorical probabilities, finding on Text8 that the spherical path gives the lowest external GPT-J NLL.	arXiv	2025.04	—
RDLM ◆	Continuous Diffusion Model for Language Modeling Places square-root-mapped categorical distributions on a hypersphere and learns a mixture of diffusion bridges toward the terminal token posterior, connecting discrete diffusion with statistical-manifold flows.	NeurIPS 2025	2025.02
Fisher-Flow ◆	Fisher Flow Matching for Generative Modeling over Discrete Data Treats categorical distributions as points on a statistical manifold with the Fisher–Rao metric, training flow matching with Riemannian optimal transport and mixing masked and uniform paths for language modeling.	NeurIPS 2024	2024.05
SFM ◆	Categorical Flow Matching on Statistical Manifolds Follows Fisher-metric geodesics on the manifold of categorical distributions with a learned tangent field, sampling each token from the squared terminal state, with Text8 and DNA experiments.	NeurIPS 2024	2024.05
BFN ◆	Bayesian Flow Networks Updates per-position categorical beliefs by Bayes' rule from noisy Gaussian evidence, starting from uniform beliefs and ending with a categorical draw, applied to character-level language modeling.	arXiv	2023.08
TESS ◆	TESS: Text-to-Text Self-Conditioned Simplex Diffusion Extends simplex logit states to full-target text-to-text generation by adapting a pretrained masked language model, with self-conditioning that averages current and previous token probabilities.	EACL 2024	2023.05
GlyphDiffusion	GlyphDiffusion: Text Generation Is Also Image Generation Renders target text as glyph images and generates them with cascaded image diffusion conditioned on the input, then recovers the final text through a text grounding module.	arXiv	2023.04	—
SSD-LM ◆	SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control Perturbs almost-one-hot vocabulary logits with Gaussian noise, projecting each prediction to a token encoding and re-noising, and generates blocks left to right with modular control from off-the-shelf classifiers.	ACL 2023	2022.10
Simplex Diffusion	Categorical SDEs with Simplex Diffusion Introduces simplex diffusion for categorical data, running independent Cox–Ingersoll–Ross processes on each coordinate and normalizing by their sum so the trajectory stays on the simplex with a Dirichlet stationary distribution.	arXiv	2022.10	—
Analog Bits ◆	Analog Bits: Generating Discrete Data Using Diffusion Models with Self-Conditioning Writes token identifiers in binary, diffuses the real-valued bits with Gaussian noise, and thresholds predictions back to tokens, introducing self-conditioning, with image captioning as its text task.	ICLR 2023	2022.08

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Contextual Encodings

Full-length contextual states from a frozen or jointly trained encoder, read out by a shared head or a separate parallel or autoregressive decoder. _{(Survey §3.2)}

Model	Paper	Venue	Date	Code
ELF (T5Gemma 2) ◆	Scaling and Distilling Text Embeddings for Better Diffusibility Scales ELF's frozen encoder from T5-small to T5Gemma-2, lowering GenPPL by about 40%, and distills it into a student encoder so fewer generated states land near no valid word.	arXiv	2026.10
DeltaFlow ◆	DeltaFlow: Noise-Adaptive Bidirectional Gated Delta Networks for Embedded Language Flows Swaps the quadratic full attention of Embedded Language Flows for a noise-adaptive bidirectional gated delta network that scans forward and backward, alternating across layers or in parallel.	arXiv	2026.08	—
TextLDM ◆	TextLDM: Language Modeling with Continuous Latent Diffusion Transfers the visual VAE-plus-DiT flow-matching recipe to text, training a one-position-per-token TextVAE whose alignment to a frozen language model barely changes reconstruction but improves continuation MAUVE.	arXiv	2026.05	—
ELF ◆	ELF: Embedded Language Flows Runs continuous-time flow matching over pretrained contextual embeddings and decodes tokens at the final step with the same network, reporting stronger few-step generation quality than discrete baselines.	NeurIPS 2026	2026.05
CoDAR ◆	CoDAR: Continuous Diffusion Language Models are More Powerful Than You Think Pinpoints token rounding as a primary bottleneck, decoding diffused token-aligned contextual states with a cross-attending autoregressive decoder and splitting the pointwise decoder's gap into conditional-dependence and locality terms.	EMNLP 2026	2026.03
Zonkey	Zonkey: A Hierarchical Diffusion Language Model with Differentiable Tokenization and Probabilistic Attention Learns tokenization end to end with a differentiable segment splitter and probabilistic attention inside a hierarchical diffusion model spanning raw characters to document-level representations.	arXiv	2026.01	—
—	A Spectral Perspective on Continuous Diffusion Language Models Analyzes continuous diffusion language models from a spectral perspective and proposes frequency-aware diffusion over continuous text representations.	ICLR 2027 submission	2026	—
Diffusion-LEF	Effective Integration of Text Diffusion and Pre-Trained Language Models with Linguistic Easy-First Schedule Integrates text diffusion with pretrained language models under a linguistic easy-first schedule, decoding through a frozen BART decoder from learned embeddings or, in a variant, frozen contextual BERT states.	LREC-COLING 2024	2024.05	—
LDP ◆	Improved Paraphrase Generation via Controllable Latent Diffusion Paraphrases by diffusing frozen BART encoder states and decoding them with the frozen BART decoder, controlling semantics through input segments alone rather than external features.	Front. Comput. Sci. 2026	2024.04	—
TEncDM ◆	TEncDM: Understanding the Properties of the Diffusion Model in the Space of Language Model Encodings Diffuses frozen contextual encodings of the target at one vector per token, regresses the clean encodings, and trains a separate bidirectional decoder to read generated states back into tokens.	AAAI 2025	2024.02
LaDiffuSeq	Utilizing Latent Diffusion Model to Accelerate Sampling Speed and Enhance Text Generation Quality Applies latent diffusion over contextual text representations to accelerate sampling and improve text generation quality.	Electronics 2024	2024	—
LDSeq	LDSeq: Latent Diffusion Models for Sequence to Sequence Text Generation Brings latent diffusion to sequence-to-sequence text generation by denoising in a contextual latent space.	CSAI 2023	2023	—

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Compressed Latent Codes

Codecs that compress text into fewer latent positions or narrower channels; a diffusion or flow prior generates the codes and a decoder realizes the text. _{(Survey §3.3)}

Model	Paper	Venue	Date	Code
PSF ◆	Rethinking the Roles of Diffusion and Decoding: Predictive-State Flows for Parallel Language Generation Divides generative roles by having a rectified-flow prior jointly generate eight predictive states per document, each encoding only preceding context, and a block decoder resolve token choices in parallel.	arXiv	2026.10	—
LLMAE ◆	Repurposing Pre-trained LLMs as High Fidelity Continuous Text Autoencoders Turns a decoder-only LLM into a continuous text autoencoder by appending 256 learned query tokens and masking upper layers to reconstruct documents from those intermediate activations via low-rank adaptation, with an image-conditioned diffusion prior generating codes for captioning.	arXiv	2026.09
JPEG-DLM ◆	One Latent, Many Tokens: Jointly Learning Compressed Embeddings for Efficient Language Diffusion Trains a Perceiver compressor over frozen T5-small features jointly with its flow model via joint-embedding prediction against an EMA target compressor, then decodes each multi-token latent in parallel.	arXiv	2026.09
AURORA ◆	AURORA-LM: Autoencoding Unified Representation for Continuous-Latent Diffusion Language Modeling Builds a full-length, prefix-aligned latent sequence with a query-based encoder-decoder, generates it with a block-causal flow-matching transformer, and retunes training noise for each latent width.	arXiv	2026.08
Manta-LM ◆	Language Generation as Optimal Control: Closed-Loop Diffusion in Latent Control Space Frames generation as stochastic optimal control, running flow matching over shortened convolutional TextVAE codes aligned to text regions and decoding tokens in parallel, with support for infilling.	arXiv	2026.05	—
LaDiff / DiLaDiff ◆	DiLaDiff: Distilled Latent-Augmented Diffusion for Language Modeling Guides masked-diffusion unmasking with a compressed continuous latent, distills the latent prior into a few-step flow map via MeanFlow, and finds stronger codec regularization improves prior samples despite worse reconstruction.	NeurIPS 2026	2026.05
Cola ◆	Continuous Latent Diffusion Language Model Pretrains a token-aligned, channel-narrowed TextVAE and then co-adapts the codec alongside a block-causal flow-matching prior over its latents for blockwise text generation.	NeurIPS 2026	2026.05
CRoCoDiL ◆	CRoCoDiL: Continuous and Robust Conditioned Diffusion for Language Conditions LLaDA's masked demasking on an ordered bank of diffused continuous summary registers via prefix embeddings for code generation, refreshing the registers once from visible tokens at mid-demasking.	arXiv	2026.03	—
Latent Thought Flows	Latent Thought Flows with Text Compression Packs 256 tokens into 8 continuous latents generated by a flow prior, showing that latent spaces should be judged by prior-generated samples rather than clean-text reconstruction alone.	Blog	2026	—
LaDiR ◆	LaDiR: Latent Diffusion Enhances LLMs for Text Reasoning Reasons through latent thought blocks, compressing each rationale step with a VAE, denoising the blocks by flow matching inside an LLM backbone, and then decoding the answer autoregressively.	ICLR 2026	2025.10	—
Cosmos ◆	Cosmos: Compressed and Smooth Latent Space for Text Diffusion Modeling Generates short code arrays in a compressed, smooth latent space learned by a separately trained deterministic autoencoder aligned to frozen language-encoder activations, then decodes all tokens in parallel.	NeurIPS 2025	2025.06
PLANNER ◆	PLANNER: Generating Diversified Paragraph via Latent Language Diffusion Model Fits a Gaussian diffusion prior to the posterior means of a pretrained, frozen variational paragraph codec, then has an autoregressive decoder realize each paragraph from the sampled latent plan.	NeurIPS 2023	2023.06
LD4LG ◆	Latent Diffusion for Language Generation Compresses pretrained encoder-decoder states into a short code array with a Perceiver resampler, diffuses those codes, and lets the model's autoregressive decoder write unconditional or seq2seq text.	NeurIPS 2023	2022.12

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Sentence and Segment Vectors

One vector per sentence or segment (for example SONAR or VAE latents), generated jointly or by next-vector prediction and decoded by a separate decoder. _{(Survey §3.4)}

Model	Paper	Venue	Date	Code
Mimir ◆	Mimir: Large-Scale Multilingual Concept Modeling Retrains the Two-Tower diffusion concept model at 1.6B parameters on SONAR embeddings of 38.9B sentences in 46 languages, then instruction-tunes it for multilingual summarization and question answering.	EMNLP 2026	2026.05	—
CALM	Continuous Autoregressive Language Models Autoencodes each K-token chunk into one continuous vector and predicts vectors autoregressively, defaulting to a one-step energy-score head but also testing multi-step diffusion and flow-matching heads.	arXiv	2025.10
SLD ◆	Segment-Level Diffusion: A Framework for Controllable Long-Form Generation with Diffusion Language Models Encodes long-form outputs as fixed-size segment latent arrays, denoises them jointly with token reconstruction losses backpropagated through a frozen decoder, and decodes segments in parallel, autoregressively within each.	ACL 2025	2024.12	—
Diffusion LCM ◆	Large Concept Models: Language Modeling in a Sentence Representation Space Models text as SONAR sentence-embedding sequences, diffusing each next concept vector and decoding it through the frozen SONAR decoder, with a 7B Two-Tower variant trained on 2.7T tokens.	arXiv	2024.12
DGLM ◆	Diffusion Guided Language Modeling Steers an autoregressive language model toward target attributes with soft prompts mapped from guided sentence-vector diffusion, training the adapter on noisy proposals to keep reliance on the latent plan adjustable.	Findings of ACL 2024	2024.08
CoDi ◆	Any-to-Any Generation via Composable Diffusion Extends Optimus sentence-latent diffusion to audio and video conditions within a composable any-to-any generator, decoding text with the VAE's GPT-2 decoder, including for image captioning.	NeurIPS 2023	2023.05
LaDiDa ◆	Latent Diffusion for Document Generation with Sequential Decoding Denoises a document's sentence vectors jointly with a self-conditioned DDPM and decodes them sequentially with a BART Vec2Seq decoder, where conditioning on preceding decoded sentences lowers sentence-level reconstruction perplexity and beats fine-tuned autoregressive baselines in MAUVE on ROCStories and Scientific Papers but not on WikiSection.	NeurIPS 2023 Workshop	2023	—
Versatile Diffusion	Versatile Diffusion: Text, Images and Variations All in One Diffusion Model Produces text inside a single image-text diffusion model by generating Optimus sentence latents under image or text conditions and decoding them with a frozen GPT-2 decoder.	ICCV 2023	2022.11

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Hybrid Continuous–Discrete States (Boundary)

Boundary systems that pair a categorical token canvas with a real-valued channel. The survey summarizes them for comparison; purely discrete diffusion models are out of scope. _{(Survey App. C.1)}

Model	Paper	Venue	Date	Code
—	Sticky Jump Diffusions: A Unifying Framework for Discrete, Continuous, and Hybrid Diffusion Recovers masked, continuous, and hybrid diffusion as limits of processes whose token-embedding anchors release mass into continuous diffusion, reversed by a score SDE with sticky jumps.	NeurIPS 2026	2026.07
x-Prediction Flow	x-Prediction Flow: Efficient Continuous Decoding for Masked Diffusion Language Models Wraps LLaDA-8B, after x-prediction alignment of the backbone, in a continuous decoder that treats mask predictions as clean-state targets for bounded Euler embedding steps, with GRPO-learned confidence-conditioned step sizes per position.	arXiv	2026.06	—
MLFM	Masked Language Flow Models Bridges partially masked and clean sequences with a continuous stochastic interpolant, bringing masking to flow language models and promoting tokens by confidence during sampling.	arXiv	2026.06
IMDM	Infinite Mask Diffusion for Few-Step Distillation Replaces the single deterministic mask with a stochastic infinite-state mask by attaching MLP-transformed uniform random vectors to unresolved positions, mitigating the factorization-error bound in few-step distillation of masked diffusion.	ICML 2026	2026.05	—
Co-LADD / Di-LADD	Latent-Augmented Discrete Diffusion Models Introduces a learnable auxiliary latent channel, continuous in Co-LADD and discrete in Di-LADD, diffused jointly with masked tokens or resolved first to capture cross-token dependencies.	ICML 2026 Workshop	2025.10	—
TDD	In-Situ Tweedie Discrete Diffusion Models Keeps diffusion in one-hot space by adding Gaussian noise to one-hot vectors and alternating cross-entropy class predictions, argmax projections, and Gaussian updates, with image captioning among its tasks.	arXiv	2025.10	—
CADD	Continuously Augmented Discrete Diffusion model for Categorical Generative Modeling Augments masked token diffusion with a paired continuous latent channel whose noisy vectors hint at unresolved positions, and adapts pretrained code backbones while selecting still-masked positions by top negative entropy.	ICLR 2026	2025.10	—
CCDD	Coevolutionary Continuous Discrete Diffusion: Make Your Diffusion Language Model a Latent Reasoner Pairs continuous diffusion with discrete token diffusion in one product state for latent reasoning, motivated by proofs that continuous diffusion is more expressive than discrete diffusion and looped transformers.	ICML 2026	2025.10
CANDI	CANDI: Hybrid Discrete-Continuous Diffusion Models Decouples discrete and continuous corruption, applying Gaussian noise while revealing committed clean tokens at random times, after a token-identifiability analysis of how Gaussian noise degrades discrete data.	ICML 2026	2025.10	—
DDOT	Flexible-length Text Infilling for Discrete Diffusion Models Enables flexible-length infilling for discrete diffusion by treating word positions as continuous variables in a product state with the discrete tokens.	EMNLP 2025	2025.06	—
VADD	Variational Autoencoding Discrete Diffusion with Enhanced Dimensional Correlations Modeling Redraws a step-local Gaussian latent at each masked-diffusion step, learned with a recognition model and variational bounds, so few-step categorical sampling can capture correlations among tokens.	ICLR 2026	2025.05	—

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⚙️ The Transition: Learning the Denoiser

How is the state revised? What the denoiser predicts, which modules are trained in which stages, and how noise schedules and self-conditioning shape training. _{(Survey §4)}

Prediction Targets and Objectives

Clean-state, noise, velocity, and token-posterior targets; endpoint token anchoring; variational and probability-flow likelihood objectives; regularizers that keep the state informative. _{(Survey §4.1)}

Model	Paper	Venue	Date	Code
ConvergeFlow ◆	ConvergeFlow: Language Flow with Provable Convergence to Token Embeddings Constrains the flow's endpoint predictor to barycenters of vocabulary embeddings, trains with flow-matching squared error alone, and proves sampling converges to valid token embeddings without a cross-entropy decoder.	arXiv	2026.08
GEXIT	Conservation Laws for Diffusion Models Derives GEXIT-based conservation laws expressing data-model cross-entropy as an integral along the noise path, unifying discrete and continuous diffusion likelihoods and recovering I-MMSE in the Gaussian case.	NeurIPS 2026	2026.07
RePlaid ◆	Continuous Diffusion Scales Competitively with Discrete Diffusion for Language Aligns Plaid with discrete-diffusion baselines for compute-matched comparison, reporting a 22.1 OpenWebText perplexity bound and an estimated 20× training-compute multiple to match autoregressive NLL.	NeurIPS 2026	2026.05	Project
—	Towards Faster Language Model Inference Using Mixture-of-Experts Flow Matching Decomposes flow-matching transport into locally specialized mixture-of-experts velocity fields, applies cross-entropy at the endpoint reached by a training rollout, and infills sparse NarrativeQA spans in four Euler steps.	arXiv	2026.04	—
LangFlow ◆	LangFlow: Continuous Diffusion Rivals Discrete in Language Modeling Connects token cross-entropy training to flow matching through a Bregman-divergence formulation, derives its continuous denoiser from predicted token probabilities with a shared vocabulary head, and constructs an ODE-based likelihood bound for evaluation.	NeurIPS 2026	2026.04
SCLM ◆	Sentence Curve Language Models Recasts Difformer's regression target as B-spline control points whose token-position values are the clean embeddings, improving English–German translation over Difformer with distillation and matching or exceeding beam-search autoregressive baselines on higher-resource benchmarks while trailing slightly on smaller setups.	arXiv	2026.02	—
SERF	Self-Regularized Flow Language Models Proposes flow language models built on a self-regularized denoiser architecture for continuous flow-based text generation.	arXiv	2026	—
—	Rectified Language Flow Reports a closed-form guarantee that its language flow converges to valid token embeddings, with singular logits absorbing the posterior's divergent part and the network predicting only a bounded residual.	arXiv	2026	—
WDR	Diverse Target Representations for Language Models with Word Difference Representations Diversifies the target representations that language models learn to predict by introducing word difference representations.	PACLIC 2025	2025.12	—
SSP	A Unification of Discrete, Gaussian, and Simplicial Diffusion Separates context prediction from local corruption evidence with a hollow parameterization and uses sufficient-statistic inputs to share one denoiser across discrete, Gaussian, and simplicial diffusion.	ICLR 2026	2025.12
DiffuER	DiffuER: Auxiliary Regularized Diffusion Model for Text Generation with Semantic Consistency Regularizes a text diffusion model with auxiliary objectives to improve the semantic consistency of generated text.	IJCNN 2025	2025	—
Masked-Diffuse LM ◆	A Cheaper and Better Diffusion Language Model with Soft-Masked Noise Groups words by relevance and entropy and corrupts the groups successively with soft-masked noise, recovering easy words first, while applying token cross-entropy across noise levels for controllable generation.	EMNLP 2023	2023.04
Difformer ◆	Empowering Diffusion Models on the Embedding Space for Text Generation Anchors learned embeddings against collapse with a vocabulary anchor loss, rescales the noise, and runs an encoder-decoder denoiser that regresses clean embeddings for translation and summarization.	NAACL 2024	2022.12

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Training Stages and Module Adaptation

Staged and co-adapted codecs, learning through frozen decoders, pretraining from scratch, adapting autoregressive or masked checkpoints, and reward-driven post-training. _{(Survey §4.2)}

Model	Paper	Venue	Date	Code
Cola2 ◆	Cola2: Co-Adaptive Hierarchical Language Modeling with Continuous Semantic Compression and Balanced Discrete Generation Generates dynamically segmented semantic-span latents with a block-causal flow prior fit to stop-gradient targets and decodes them with a block-causal masked-diffusion decoder, while the codec keeps token-prediction, KL-regularization, and span-duration objectives.	arXiv	2026.10	—
CFRL	Backpropagating Verifier Rewards Through Continuous Flow Language Models Backpropagates verifier rewards into continuous flow language models through a critic on intermediate ELF states and one stochastic denoiser step, outperforming group-relative REINFORCE on synthetic reasoning puzzles.	arXiv	2026.10	—
DSL-LLaDA ◆	DSL-LLaDA: Scaling Continuous Denoising to 8B Masked Diffusion LMs Converts masked LLaDA-8B-Instruct to continuous embedding-space denoising with 1,000 continued-pretraining steps under continuous per-token noise, consistently improving short- and medium-input summarization over the original across evaluation budgets.	Findings of EMNLP 2026	2026.06	—
LDLM ◆	How to Train Your Latent Diffusion Language Model Jointly With the Latent Space Adapts an encoder, decoder, and diffusion denoiser jointly on frozen pretrained contextual features, and shows that raising decoder input noise lowers GenPPL while collapsing MAUVE and entropy.	NeurIPS 2026	2026.05	—
—	Training Latent Language Diffusion Models Requires Less Than You Think Shows with LDLM-s that jointly training encoder, prior, and decoder from random initialization, without a separate stage-1 pretraining phase, can improve the OpenWebText GenPPL–entropy trade-off over the pretrained-feature baseline ELF-B in their overlapping entropy range.	ICLR 2027 submission	2026	—
GENIE ◆	Text Generation with Diffusion Language Models: A Pre-training Approach with Continuous Paragraph Denoise Pretrains an encoder and cross-attending embedding denoiser by continuous paragraph denoising, reconstructing masked paragraph spans from the surrounding document via noise prediction, and applies the model to summarization and CommonGen.	ICML 2023	2022.12
LDEBM ◆	Latent Diffusion Energy-Based Model for Interpretable Text Modeling Couples a sentence encoder and autoregressive decoder with a Gaussian diffusion prior whose energy-based reverse conditionals use short-run Langevin sampling, trained jointly for interpretable text modeling.	ICML 2022	2022.06

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Noise Schedules and Self-Conditioning

Noise calibrated to the embedding geometry, time reweighting, position- and content-dependent schedules, learned forward paths, depth-specialized denoisers, and self-conditioning. _{(Survey §4.3)}

Model	Paper	Venue	Date	Code
DoubleCat / SemiCat ◆	On the Design Space of Continuous Diffusion Language Models Explains self-conditioning as correcting a train–inference mismatch and recovers its gain without a second pass by corrupting the simplex endpoint (DoubleCat), while analyzing how cross-entropy shapes embedding geometry.	arXiv	2026.10	—
LangDiT ◆	Designing Transformers for Continuous Diffusion Language Models Redesigns the Transformer denoiser for continuous diffusion language models with normalization, wider noise conditioning, and entropy-gated self-conditioning, the gate giving the largest single improvement in generative perplexity in LangFlow ablations.	arXiv	2026.10	—
TTCD ◆	Token Time Continuous Diffusion for Language Modeling Assigns each token its own time via entropy ranking in a deterministic continuous diffusion, and shortcut training cuts OpenWebText prefix-continuation GenPPL from 1033.8 to 437.82 at four updates.	NeurIPS 2026	2026.07	—
—	A Dominant Self-Conditioning Direction Drives Repetition in Unconditional Continuous Diffusion Language Models Traces repetition under heavily weighted self-conditioning feedback to a dominant one-dimensional attractor and counters it with the training-free Attractor-Contrast-Escape (ACE) correction, showing in its original arXiv version that scoring a low-repetition accepted subset reverses the ELF-B/ELF-M ranking.	arXiv	2026.07
BlockTrain	Decentralised AI Training and Inference with BlockTrain Distributes noise-range-specialized Transformer blocks, as in DiffusionBlocks, across decentralized workers for byte-level modeling, feeding expected embeddings back at inference and nearly matching an end-to-end Transformer's cross-entropy.	arXiv	2026.06	—
—	Why Gaussian Diffusion Models Fail on Discrete Data and How to Prevent It? Shows with a toy hierarchical model that learned denoising errors and time discretization can push DDPM trajectories into low-density regions between modes while the optimal conditional-mean predictor recovers valid samples, and improves sampling by combining self-conditioning with q-sampling.	COLM 2026	2026.04	—
InfoNoise	Noise Scheduling as Information-Guided Allocation in Diffusion Training Reallocates diffusion training effort online toward informative noise levels, estimating a conditional-entropy-rate profile from denoising losses via I-MMSE and changing only the noise distribution.	arXiv	2026.02	—
—	Towards Latent Diffusion Suitable For Text Extends Neural Flow Diffusion Models to language, learning the forward noising path jointly with embeddings and denoiser, though few-step generation does not beat a fixed-schedule Diffusion-LM baseline.	arXiv	2026.01
—	Calibrating Noise Schedules for Continuous Language Diffusion with Token Uncertainty Calibrates noise schedules for continuous language diffusion without querying a denoiser, estimating conditional token entropy under Gaussian corruption from unigram frequencies and embedding geometry to shift training and sampling log-SNR levels, so calibrated FLM-B reaches LM1B GenPPL 94.73 in 256 steps versus 97.95 for the uncalibrated 1024-step baseline.	ICLR 2027 submission	2026	—
OFE+STDL	Timestep Embeddings Trigger Collapse in Diffusion Text Generation Identifies timestep embeddings as a trigger of collapse in diffusion text generation and proposes the OFE+STDL remedy to prevent it.	CoNLL 2025	2025.07	—
NeoDiff ◆	Unifying Continuous and Discrete Text Diffusion with Non-simultaneous Diffusion Processes Assigns each token its own diffusion progress, predicted from the current estimate, in a non-simultaneous Gaussian embedding process with an optimized time grid for translation and other seq2seq tasks.	ACL 2025	2025.05
Meta-DiffuB ◆	Meta-DiffuB: A Contextualized Sequence-to-Sequence Text Diffusion Model with Meta-Exploration Lets the source sentence set the noising schedule through a meta-learned scheduler that explores contextualized schedules for a seq2seq embedding diffusion model.	NeurIPS 2024	2024.10
SeqDiffuSeq ◆	Text Diffusion Model with Encoder-Decoder Transformers for Sequence-to-Sequence Generation Encodes the source once with an encoder–decoder Transformer whose target denoiser attends to it, learning position-specific noise schedules from denoising losses and self-conditioning on previous clean estimates.	NAACL 2024	2024.06
TREC	Text Diffusion with Reinforced Conditioning Rewards the BLEU gain that self-conditioning feedback achieves over an unconditioned pass, a time-aware reinforcement scheme for sequence-to-sequence embedding diffusion.	AAAI 2024	2024.02	—
InfoDiffusion ◆	InfoDiffusion: Information Entropy Aware Diffusion Process for Non-Autoregressive Text Generation Schedules per-word noise by information content, keeping high-information words visible longer in the forward process so they are recovered earlier in reverse seq2seq generation.	Findings of EMNLP 2023	2023.10
DiNoiser ◆	DINOISER: Diffused Conditional Sequence Learning by Manipulating Noises Restricts training to noise levels above an embedding-separability threshold and inflates the noise level fed to the denoiser at inference, so the conditional denoiser must use source information in translation and paraphrasing.	TACL 2024	2023.02

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🚀 Sampling, the Text Interface, and Generation Order

Where do words enter? Samplers and few-step routes, the text interface, generation order, and guidance. _{(Survey §5)}

Samplers and Few-Step Generation

Solvers, bridges, and adaptive step allocation; training for coarse updates; finite-interval flow maps; distribution-matching and score-identity distillation; drifting. _{(Survey §5.1)}

Model	Paper	Venue	Date	Code
ELF-MMD ◆	Representation-Space MMD for Diffusion Language Models Minimizes kernel MMD between generated and real latents in a frozen ELF model's feature space to train few-step ELF generators without a score network, lowering GenPPL at comparable entropy.	arXiv	2026.10
ReLaDrift	ReLaDrift: Recurrent Language Generation via Drifting for Test-Time Scaling Iterates a shared drifting generator to refine a noise-initialized draft in continuous latent space, trained over sampled round counts so extra rounds trade computation for quality.	arXiv	2026.10
ReSFlow	Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation Rectifies continuous flows on statistical manifolds into geodesic, reflow-style trajectories that respect the intrinsic Riemannian geometry, enabling one-step categorical generation.	NeurIPS 2026	2026.10
Seq-Drifting ◆	One-Step Text Generation by Seq-Drifting Maps Gaussian noise to continuous token embeddings in one pass, training the generator on a drift field that attracts outputs toward contextually plausible tokens and repels collapse and repetition.	arXiv	2026.10
GSF ◆	Gumbel Straight Flow: Distilling Autoregressive Models into One-step Flow Maps Pairs Gumbel noise with sequences from a pretrained autoregressive teacher along non-intersecting straight paths, supervising a one-step flow map whose longer intervals are trained by a semigroup loss.	arXiv	2026.10	—
BCT ◆	BCT: Bayes-Consistent Tempering for Flow Language Models Makes temperature consistent across the endpoint, bridge, and velocity of posterior-induced flow language models, substantially improving S-FLM's low-temperature math reasoning accuracy over standard tempering and narrowing the gap to discrete diffusion.	arXiv	2026.10	—
—	Adaptive Second-Order Solvers for Fast Stochastic Diffusion Sampling Controls step sizes of second-order stochastic diffusion solvers with a proportional-integral rule on noise-normalized error, and aggregates per-sample trajectories into a fixed schedule for image and language data.	arXiv	2026.10
StepTune ◆	A Step in the Right Place: Understanding and Optimizing Timestep Placement in Continuous Diffusion Language Models Searches timestep grids for frozen ELF models using terminal-latent error and decoder KL against finer trajectories, with a 16-step grid matching or exceeding the native 64-step grid on summarization and translation at a fraction of the batch-1 latency.	arXiv	2026.10
Simplex-DMD / Reinforced-DMD ◆	Distribution Matching Distillation for Continuous Diffusion Language Models Distills continuous diffusion language models into few-step students by reverse-KL distribution matching, using simplex relaxations with pathwise gradients or categorical draws with REINFORCE and a density ratio.	arXiv	2026.09	—
DBTM ◆	Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning Learns a time-independent map sending any point to its simplex vertex by minimizing a conservation-equation residual from data, enabling one-step or iterated generation without a teacher or time input.	arXiv	2026.09	—
Untied Self-Conditioning ◆	Improving Few-Step Language Flows with Untied Self-Conditioning Lowers eight-step GenPPL on frozen ELF and LangFlow checkpoints by combining a history-averaged solver correction with damped self-conditioning feedback, at the cost of higher four-gram repetition.	arXiv	2026.08	—
Self-Conditioned FMLM ◆	Self-conditioned Flow Map Language Models via Fixed-point Flows Recasts self-conditioning in flow language models as fixed-point iteration and distills fixed-point flows into one-step flow maps whose GenPPL falls as more refinements build the targets.	arXiv	2026.07
—	Why Do Few-Step Text Latents Fail When Image Latents Work? Non-Commitment at Sharp Categorical Readouts Traces few-step failure on text latents to sampler residuals that align with low-margin decoder directions, showing that ELF and LangFlow residuals flip more decoded tokens than norm-matched isotropic noise.	arXiv	2026.06	—
Scaling CatFM ◆	Scaling Categorical Flow Maps Scales simplex flow matching to a 1.7B-parameter model trained from scratch on 2.1T tokens, then progressively self-distills a two-time flow map that recovers conditional MAUVE at four updates, while trailing MDLM and Duo on zero-shot multiple-choice QA.	arXiv	2026.05	—
MCB ◆	Sampling from Flow Language Models via Marginal-Conditioned Bridges Samples one-hot endpoints from a flow language model's token marginals and draws each next state from an Ornstein–Uhlenbeck bridge, preserving entropy on coarse grids without retraining.	arXiv	2026.05
FlowLM	FlowLM: Few-Step Language Modeling via Diffusion-to-Flow Adaptation Fine-tunes pretrained diffusion language models into straight-path flow-matching models with a clean-data prediction objective, reporting few-step quality that rivals 2,000-step diffusion sampling.	WAICA 2026	2026.05	—
FastDiSS ◆	FastDiSS: Few-step Match Many-step Diffusion Language Model on Sequence-to-Sequence Generation Computes training-time self-conditioning feedback from a more heavily corrupted state, so a seq2seq embedding denoiser learns not to over-rely on imperfect drafts when sampling in few steps.	Findings of ACL 2026	2026.04	—
DFM ◆	Discrete Flow Maps Aligns flow-map training with probability-simplex geometry instead of Euclidean regression, with progressive self-distillation keeping entropy near many-step levels where the Eulerian variant collapses.	arXiv	2026.04	—
FMLM ◆	Flow Map Language Models: One-step Language Modeling via Continuous Denoising Parameterizes flows and flow maps over one-hot token states with a simplex-valued output head, distilling one-step maps that keep entropy near many-step levels at higher generative perplexity.	NeurIPS 2026	2026.02
CatFM ◆	Categorical Flow Maps Self-distills a flow map toward the probability simplex that transports mass to a predicted endpoint, enabling few-step categorical generation and guidance, with the final published one-step LM1B result at GenPPL 142.7 and entropy 4.03.	ICML 2026	2026.02	—
—	Understanding and Enabling Score Distillation in Continuous Diffusion Language Models Analyzes score distillation for continuous diffusion language models and proposes modifications that enable it to produce few-step generators.	ICLR 2027 submission	2026	—
AIM-FLM	The Denoising Estimate Is a State Variable: Joint Refinement for Few-Step Flow Language Models Treats the denoising estimate as a state variable refined jointly with the noisy sequence, an implicit-midpoint-style design for few-step flow language models.	ICLR 2027 submission	2026	—
RCFG ◆	Reliability-Calibrated Guidance for Few-Step Categorical Flow-Map Text Generation Steers a pretrained Categorical Flow Map toward target attributes and words with reliability-calibrated guidance, adding control to few-step simplex generation without retraining the map.	Findings of EMNLP 2026	2026	—
—	Reading Latent States: Adaptive Halting in Continuous Diffusion Language Models Proposes adaptive halting for continuous diffusion language models, reading the evolving latent states to decide when sampling can stop early.	ICLR 2027 submission	2026	—
—	Latent Space Co-training for Few-Step Text Generation Distills a two-time flow map in a compressed latent diffusion space while briefly co-training the latent encoder with a tracking teacher and an encoder anchor, improving few-step OpenWebText generation and GSM8K Python-solution accuracy over prior flow-map baselines.	NeurIPS 2026 Workshop	2026	—
INCO ◆	Inverse-Confidence Sampling for Continuous Diffusion Language Models Modifies only the sampler of continuous diffusion language models with inverse-confidence sampling, cutting LangFlow's 1024-step OpenWebText GenPPL from 36.7 to 28.1 as entropy shifts from 5.25 to 5.18.	ICML 2026 Workshop	2026	—
—	How to Train Your Latent Flow Map for Few-Step Text Generation Studies how to train latent flow maps for few-step text generation, comparing a frozen encoder and teacher (LDLM-FM) with jointly adapting both (LDLM-FM-A), which can improve multi-sample coverage without improving single-sample accuracy.	ICLR 2027 submission	2026	—
—	Asynchronous Flow Maps for Flow Language Models Introduces asynchronous flow maps for flow language models, extending finite-interval flow-map transport for few-step text generation.	ICLR 2027 submission	2026	—
DLM-One ◆	DLM-One: Diffusion Language Models for One-Step Sequence Generation Compresses a pretrained continuous diffusion language model into a one-step generator by Score identity Distillation in embedding or logit space, reporting up to about 2000× fewer sampling steps.	arXiv	2025.06	—
Logit-KL FM	Logit-KL Flow Matching: Non-Autoregressive Text Generation via Sampling-Hybrid Inference Formulates flow matching for non-autoregressive text in logit space and compares deterministic, re-noised, and mixed sampling updates within one unified logit framework.	ICLR 2026	2024.11	—
LanguageFlow ◆	LanguageFlow: Advancing Diffusion Language Generation with Probabilistic Flows Learns few-step source-to-target flow-matching transport in a VAE latent space, using ten Euler updates followed by autoregressive decoding of the transported codes for sentiment transfer.	NAACL 2024	2024.06	—
Temporal Pruning ◆	Few-shot Temporal Pruning Accelerates Diffusion Models for Text Generation Prunes a trained DiffuSeq sampling chain to a few optimized timesteps, degrading less than uniform subsampling while still falling short of the full-length chain's quality.	LREC-COLING 2024	2024.05
BFN-Solver ◆	Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations Derives an SDE for the Gaussian logits underlying Bayesian Flow Network categorical beliefs, so higher-order solvers can sample a pretrained BFN in fewer steps without retraining, tested on text8.	ICML 2024	2024.04
FlowSeq ◆	Flow Matching for Conditional Text Generation in a Few Sampling Steps Trains a source-conditioned flow-matching velocity with extrapolated-endpoint supervision so one Euler step reaches an embedding sequence, approaching 2,000-step DiffuSeq in question-generation BLEU and slightly exceeding its ROUGE-L under MBR while trailing in BERTScore and on paraphrasing.	EACL 2024	2024.03
DiffuSeq-v2 ◆	DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models Replaces a time-dependent subset of noised target embeddings with a learned absorbing vector and samples with multistep DPM-Solver++, reporting few-step sequence-to-sequence generation without MBR selection.	Findings of EMNLP 2023	2023.10
DDLM ◆	Diffusion Language Models Generation Can Be Halted Early Halts sampling of continuous diffusion language models early by estimating when generation is complete, with adaptive criteria evaluated on Plaid, SSD, and CDCD models.	arXiv	2023.05	—
BG-DiffuSeq	Can Diffusion Model Achieve Better Performance in Text Generation? Bridging the Gap between Training and Inference! Post-trains a converged seq2seq embedding-diffusion denoiser for consistency between forward-noised and model-generated reverse states, then allocates the retained steps by Adaptive Decay Sampling.	Findings of ACL 2023	2023.05	—

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From States to Tokens

Clamping, projection, and expected embeddings; intermediate commitment versus remasking; shared, parallel, and autoregressive decoders for generated states. _{(Survey §5.2)}

Model	Paper	Venue	Date	Code
HC-DLM ◆	Hierarchical Continuous Diffusion Language Models Carries only a continuous latent between flow-matching steps, conditioning each update on a re-noised argmax token scaffold whose removal sharply degrades combinatorial puzzle accuracy.	arXiv	2026.10
GRAFT ◆	GRAFT: Restoring the Missing Sampling Interface in Continuous Diffusion Language Models Holds mid-sampling rare-word candidates from frozen ELF and LangFlow vocabulary heads as conditions and restarts from the same noise, restoring rare-word frequencies to near-human rates.	arXiv	2026.10	—
Posterior Refinement ◆	Posterior Refinement: Fast Language Generation via Any-Order Flow Maps Equips flow map language models with masking-style noise schedules and per-token posterior consistency scores, then commits selected endpoint predictions between flow-map rounds and re-noises the rest.	arXiv	2026.06
—	Continuous Language Diffusion as a Decoder-Interface Problem Frames continuous language diffusion as a decoder-interface problem, tracing reliable ELF denoising to decoder basins, and shows literal early-exit monitoring saves denoiser calls yet increases elapsed time.	arXiv	2026.06	—
STAR-LDM	Stop-Think-AutoRegress: Language Modeling with Latent Diffusion Planning Pauses autoregressive generation to refine a semantic continuation plan by latent diffusion, mapping it into soft prompts the integrated backbone follows, and supports attribute steering via lightweight classifiers.	COLM 2025	2026.02
CoM-DAD	Bridging the Discrete-Continuous Gap: Unified Multimodal Generation via Coupled Manifold Discrete Absorbing Diffusion Decouples semantic planning from token synthesis for unified multimodal generation, diffusing a continuous sentence-level plan and realizing it through an absorbing discrete-diffusion decoder.	arXiv	2026.01	—

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Generation Order and Length

Full-sequence refinement, blockwise and next-token orders, semi-autoregressive caching, sentence-level recurrence, length control, and length extrapolation. _{(Survey §5.3)}

Model	Paper	Venue	Date	Code
RangeSWA	RangeSWA: Training-Free Length Extrapolation for Continuous Diffusion Language Models Extends continuous diffusion language models beyond their training sequence length with a training-free length-extrapolation method applied at inference.	ARR submission	2026.10	—
Plan Canvas	Plan Canvas: Fixed Reasoning Regions for Continuous Language Flows Reserves a fixed-capacity planning region in ELF's canvas so answers start at a fixed position, and with separate plan and answer denoising clocks improves both answer accuracy and reasoning-trace validity on synthetic reasoning.	arXiv	2026.10	—
Lafa ◆	Large Flow Language Models Adapts pretrained autoregressive checkpoints into blockwise asynchronous flow models up to 8B whose own next-token head verifies flow drafts, reaching 2.54× the tokens per second of HuggingFace greedy decoding.	arXiv	2026.10
BLD ◆	Denoising Blocks, Not Tokens: Efficient Compressed Continuous Diffusion with Branching Token Realization Compresses 1024 tokens into 64 block latents generated by flow matching, then realizes each latent with a local autoregressive branch, running all branches in parallel.	arXiv	2026.10	—
Clock Diffusion ◆	Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Models Runs every position on one clock offset by position-specific phases, trained under a variational bound, giving Gaussian embedding diffusion block or sliding-window generation with key–value caching and variable-length outputs.	arXiv	2026.10	—
EFlow / EFM ◆	Expanding Flow Maps Makes length part of the generative trajectory by inserting positions into gaps of a growing array with local denoising clocks, then distills it into few-step expanding flow maps.	NeurIPS 2026	2026.07	—
—	Length from the Latents: Dynamic-Length Compressed Latent Diffusion Models Predicts output length from denoised compressed latents and masks the decompressor so each output sees all latents but only earlier outputs, enabling prefix-consistent, cache-extensible decoding.	ICLR 2027 submission	2026	—
DiffusionBlocks ◆	DiffusionBlocks: Block-wise Neural Network Training via Diffusion Interpretation Partitions the noise schedule into equal-probability intervals, each handled by an independently trained Transformer layer group that refines the next-token embedding, enabling block-wise training without end-to-end backpropagation.	ICLR 2026	2025.06
L2D ◆	Large Language Models to Diffusion Finetuning Attaches a low-rank-adapted diffusion branch to a frozen causal language model to refine each next-token embedding conditioned on a clean causal prefix, so accuracy rises with more diffusion steps.	ICML 2025	2025.01
SSD-2	David helps Goliath: Inference-Time Collaboration Between Small Specialized and Large General Diffusion LMs Scales blockwise simplex-logit diffusion to 13B from OPT-13B and shows that inference-time logit-level collaboration with a domain expert improves automatic relevance and factuality over standalone generation, unlike token-level collaboration between OPT models.	NAACL 2024	2023.05
AR-Diffusion ◆	AR-Diffusion: Auto-Regressive Diffusion Model for Text Generation Gives each token a position-dependent diffusion time so earlier positions become clean sooner and guide later ones, with a position-aware skipping sampler using as few as 20 steps.	NeurIPS 2023	2023.05

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Conditioning and Guidance

Classifier and classifier-free guidance, gradient and probe guidance, formal-syntax constraints, particle selection, and speculative drafting with flow maps. _{(Survey §5.4)}

Model	Paper	Venue	Date	Code
Noise Your Prompt ◆	Noise Your Prompt: Noising Conditioning Tokens in Continuous Diffusion Language Models Noises a flow language model's prompt to the response's noise level on a fraction of training examples, substantially improving combinatorial puzzle accuracy and summarization quality–diversity frontiers but not open-domain dialogue.	TMLR 2026	2026.10
FlashMap ◆	FlashMap: Flow Map Speculative Decoding Drafts 16-token speculative blocks in one or two steps with a flow map conditioned on a Qwen3 target's hidden states, delivering multi-fold wall-clock speedups while preserving the target's exact output distribution.	arXiv	2026.10
Probe Guidance ◆	How to Guide Your Language Flow Derives an autoguidance-style weak prediction from a small MLP probe on frozen early-layer states, lowering generative perplexity at matched entropy and improving zero-shot multiple-choice accuracy for negligible extra FLOPs.	arXiv	2026.09	—
Diffinity ◆	Continuous Diffusion Models Can Obey Formal Syntax Guides Plaid sampling toward regular-expression constraints without training, replacing the classifier with a token-aligned finite automaton whose exact log-acceptance gradients come from dynamic programming.	ICML 2026	2026.02
—	Control Enters Through the Memory: Self-Conditioning as a Control Interface in Continuous Language Flows Writes the decoder's reward gradient into a continuous language flow's self-conditioning memory at each intermediate step, without a state push, improving held-out keyword coverage over state guidance at approximately equal wall-clock cost.	ICLR 2027 submission	2026	—
LQG	Choose Before You Decode: Latent Q-Guided Generation for Diffusion Language Models Scores candidate latent states of a diffusion language model with a Q-function, pruning low-value candidates so the choice is made before decoding to text.	ICLR 2027 submission	2026	—
GuideDiffuSeq	Understanding the Quality-Diversity Trade-off in Diffusion Language Models Tunes the quality–diversity trade-off of embedding-space sequence-to-sequence diffusion with classifier-free guidance and stochastic clamping, giving a temperature-like knob that can improve generation quality.	arXiv	2025.03
FK Steering ◆	A General Framework for Inference-time Scaling and Steering of Diffusion Models Resamples intermediate diffusion states by reward in a general inference-time steering framework that, on SSD-LM text generation, beats best-of-n at equal particle count on the targeted reward.	ICML 2025	2025.01
P3SUM	P³Sum: Preserving Author's Perspective in News Summarization with Diffusion Language Models Preserves the author's perspective in news summarization by backpropagating off-the-shelf classifier gradients through expected embeddings into a diffusion summarizer's token logits between denoising updates.	NAACL 2024	2024
ParaGuide ◆	ParaGuide: Guided Diffusion Paraphrasers for Plug-and-Play Textual Style Transfer Refines target embeddings with a RoBERTa-based denoiser conditioned on a fixed autoregressive paraphrase under off-the-shelf style-classifier gradients, showing stronger guidance raises held-out style accuracy but lowers semantic similarity.	AAAI 2024	2023.08

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🎯 Tasks and Applications

Downstream capabilities, from the six capability reviews of §6.1 and the extended catalog in Appendix G. _{(Survey §6.1, App. G)}

Controllable Generation and Editing

Attribute, syntax, and style control; source-preserving editing and style transfer; detoxification, steganography, watermarking, and red-teaming. _{(Survey §6.1.1, App. G.1)}

Model	Paper	Venue	Date	Code
—	Diffusion Language Models for Perplexity-Aware Black-Box Attacks Replaces the random latent-to-token mapping of continuous-space black-box attacks with a continuous diffusion language model, sampling or optimizing its Gaussian latents to find natural, perplexity-aware adversarial prompts.	arXiv	2026.10	—
StyleShield	StyleShield: Exposing the Fragility of AIGC Detectors through Continuous Controllable Style Transfer Exposes AIGC-detector fragility through flow-matching style transfer in continuous token-embedding space, using a DiT with adapters conditioned on frozen Qwen-7B features and SDEdit-style inference.	arXiv	2026.05	—
—	Style Transfer as Bias Mitigation: Diffusion Models for Synthetic Mental Health Text for Arabic Recasts gender-bias mitigation as male-to-female style transfer, training pretraining-free diffusion models on the CARMA Arabic mental-health corpus to augment underrepresented female-authored text.	arXiv	2026.01	—
COMPASS	Watermarking Continuous Diffusion Language Models Embeds provenance watermarks in text from continuous diffusion language models by steering latent anchors.	ICLR 2027 submission	2026	—
—	Recovering Control from Compact Codes: Residual Control in Diffusion Language Models Proposes compact-code residual control, a control interface for diffusion language models that generate compact codes.	ICLR 2027 submission	2026	—
—	Knowledge-guided diffusion for emotion and topic controllable text generation Controls the emotion and topic of generated text jointly with a diffusion denoiser conditioned on knowledge guidance.	iScience 2026	2026	—
DLMDC	DLMDC: A Method for Controllable Text Generation Uses a DistillClassifier to reduce guidance-gradient noise during non-autoregressive continuous diffusion denoising for controllable text generation.	ICASSP 2026	2026	—
—	Debiased controllable text generation with classifier-guided rectified flow language model Guides a rectified-flow language model with adversarially trained classifiers in latent space for debiased controllable text generation.	J. Korean Stat. Soc. 2026	2026	—
SynText / STDiff	Syntax-Guided Diffusion Language Models with User-Integrated Personalization Conditions diffusion text generation on syntactic guidance, produced in a first stage by a cascaded design or inside a non-cascaded architecture, and on user information for personalization.	arXiv	2025.10
TTA-Diffusion	Don't Let It Fade: Preserving Edits in Diffusion Language Models via Token Timestep Allocation Counters update forgetting, where uniform denoising updates erase earlier semantic edits, using per-token timestep schedules that freeze critical tokens early while uncertain tokens keep refining.	NeurIPS 2025	2025.10	—
RegDiff	Controllable Stylistic Text Generation with Train-Time Attribute-Regularized Diffusion Regularizes a v-parameterized latent text denoiser with a frozen attribute-classifier loss in training, improving GYAFC style-transfer accuracy up to an intermediate regularization weight beyond which semantic similarity and fluency degrade, without sampling-time classifier gradients.	arXiv	2025.10	—
Babel	Mitigating Stylistic Biases of Machine Translation Systems via Monolingual Corpora Only Corrects stylistic bias in machine translation via post-processing, where a style detector flags disparities and a gradient-steered diffusion applicator rectifies them using only monolingual corpora.	arXiv	2025.07	—
PromptDiffusion	Prompt Guided Diffusion for Controllable Text Generation Enforces constraints in controllable text generation by conditioning a diffusion language model's denoiser on prompts that encode the desired control.	W-NUT 2025	2025.05	—
GTSD	GTSD: Generative Text Steganography Based on Diffusion Model Hides secret messages in text generated by a diffusion model, using seeded parallel batches instead of word-by-word candidate encoding to improve speed, robustness, and imperceptibility.	ICONIP 2025	2025.04	—
EdiText ◆	EdiText: Controllable Coarse-to-Fine Text Editing with Diffusion Language Models Performs coarse-to-fine controllable editing by partially noising a source sentence's compressed latent codes and denoising them toward a target attribute, with a separate autoregressive decoder.	ACL 2025	2025.02	—
DiffusionAttacker	DiffusionAttacker: Diffusion-Driven Prompt Manipulation for LLM Jailbreak Manipulates prompts for LLM jailbreaking with a gradient-steered diffusion paraphrase editor that rewrites the source prompt while preserving its meaning.	EMNLP 2025	2024.12	—
EDDPMs ◆	Unified Generation, Reconstruction, and Representation: Generalized Diffusion with Adaptive Latent Encoding-Decoding Trains an adaptive encoder jointly with a Gaussian diffusion denoiser over sentence latents, decoded by a separate autoregressive decoder, to unify generation, reconstruction, and representation.	ICML 2024	2024.02
QE-CDLM	Quantized Embedding Vectors for Controllable Diffusion Language Models Quantizes the task-specific embedding space of a controllable diffusion language model, refining token-level gradient steering with quantized-embedding guidance while targeting portability, stability, and inference speed.	arXiv	2024.02	—
DeTiME	DeTiME: Diffusion-Enhanced Topic Modeling using Encoder-decoder based LLM Enhances topic modeling with diffusion over sentence-level latents of an encoder–decoder LLM, structuring the global latent space with topic priors for topic-based text generation.	Findings of EMNLP 2023	2023.10
PoetryDiffusion	PoetryDiffusion: Towards Joint Semantic and Metrical Manipulation in Poetry Generation Generates poetry with a constraint-conditioned diffusion denoiser that jointly manipulates semantic content and metrical form, enforcing prosodic structure during denoising.	AAAI 2024	2023.06	—
DiffuDetox	DiffuDetox: A Mixed Diffusion Model for Text Detoxification Treats text detoxification as source-preserving editing, using a mixed diffusion model to rewrite toxic input sentences into non-toxic text.	Findings of ACL 2023	2023.06
—	Fine-grained Text Style Transfer with Diffusion-Based Language Models Learns fine-grained text style transfer with a diffusion language model trained on limited StylePTB data without external knowledge, covering individual and compositional transfers.	RepL4NLP 2023	2023.05	—

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Sequence-to-Sequence Generation

Source-conditioned transformation: translation, summarization, paraphrase, question generation, and data-, table-, or graph-to-text generation. _{(Survey §6.1.2, App. G.2)}

Model	Paper	Venue	Date	Code
DLM4G	Factual and Edit-Sensitive Graph-to-Sequence Generation via Graph-Aware Adaptive Noising Verbalizes knowledge graphs and molecules by graph-conditioned text diffusion, adaptively noising aligned entity and relation tokens by per-token denoising error to preserve structure and support localized edits.	arXiv	2026.04	—
ShortcutFlow ◆	One-step Nonautoregressive Natural Language Generation with Shortcut Flow Matching Models Learns shortcut flow maps over token embeddings on finite time intervals for one-step non-autoregressive generation, substantially improving single-step paraphrasing over ordinary flow matching, with diminishing returns at larger step budgets.	ACL 2026	2026
DiFRa	DiFRa: A Unified Framework for Harmonizing Semantic Diversity and Factual Consistency in Question-Answer Generation Balances semantic diversity and factual consistency in question–answer generation by diffusing compact conditions that guide a downstream decoder.	Findings of ACL 2026	2026
Ideation	Ideation: Diversifying Ad Text Generation in Sponsored Search with Latent Diffusion Diversifies sponsored-search ad text generation with a conditional latent diffusion model that denoises continuous text representations into varied ad creatives.	WWW 2025 Companion	2025	—
EmbDiffounder	EmbDiffounder: Semantic-Transfer Enhanced Sequence Diffusion Model for Text Generation Enhances sequence diffusion text generation with semantic transfer from M2Emb text embeddings, adding adaptive clustering and multi-scale residual fusion.	IEEE Access 2025	2025	—
DQG-DM	Diversify Question Generation Based on Diffusion Model in Dialogue Promotes diverse question generation in dialogue by having a diffusion model produce compact conditions that steer a downstream decoder.	IEICE Trans. 2025	2025	—
—	Table-to-Text Generation with Pretrained Diffusion Models Adapts the pretrained GENIE diffusion model to table-to-text generation, analyzing DPM-Solver++ sampling, ROVER and MBR aggregation, pretraining, length constraints, and diversity against autoregressive baselines.	IEEE Access 2024	2024.09	—
—	Factuality Guided Diffusion-Based Abstractive Summarization Applies factuality guidance between the denoising updates of an AR-Diffusion abstractive summarizer to keep generated summaries factually consistent with the source.	IEEE Access 2024	2024	—
FMSeq ◆	Enable Fast Sampling for Seq2Seq Text Diffusion Accelerates seq2seq text diffusion with flow matching, recovering much of its many-step baseline's quality in a few steps on question generation, paraphrasing, and simplification, while single-step generation degrades on open-ended dialogue.	Findings of EMNLP 2024	2024	—
—	Conditional Question Generation Model Based on Diffusion Model Performs conditional question generation with a diffusion model that directly denoises continuous text vectors before rounding them to tokens.	ACSS 2024	2024	—
—	Benchmarking Diffusion Models for Machine Translation Benchmarks randomly initialized Diffusion-LM and DiffuSeq on reduced CoVoST De–En translation, where they trail autoregressive and Levenshtein Transformer baselines even after distillation and degrade faster with source length.	EACL 2024	2024	—
QFS-DLM	Diffusion Language Model with Query-Document Relevance for Query-Focused Summarization Summarizes documents with respect to a query by refining target token embeddings in a diffusion language model informed by query–document relevance.	Findings of EMNLP 2023	2023.12	—
DiffuSIA	DiffuSIA: A Spiral Interaction Architecture for Encoder-Decoder Text Diffusion Introduces a spiral interaction architecture for encoder-decoder text diffusion, whose reciprocal source–target attention lets the conditional encoder also capture information about the target text.	arXiv	2023.05	—
DiffusionRet	DiffusionRet: Diffusion-Enhanced Generative Retriever using Constrained Decoding Enhances generative retrieval by using a diffusion model to generate pseudo-documents that a downstream retriever consumes through constrained decoding.	Findings of EMNLP 2023	2023	—
DiffuD2T	DiffuD2T: Empowering Data-to-Text Generation with Diffusion Splits data-to-text generation between a diffusion model that produces compact conditions and a downstream decoder that turns them into text.	Electronics 2023	2023	—

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Captioning and Multimodal Generation

Image, video, audio, and speech captioning; cross-modal bridges; and joint any-to-any generators that keep a continuous text channel. _{(Survey §6.1.3, App. G.3)}

Model	Paper	Venue	Date	Code
MUNITE	MUNITE: Unified Multimodal Latent Inference for Any-to-Any Multimodal Generation Casts encoding and latent generation as a single conditional flow over a shared latent given any observed modality subset, with modality-specific generative decoders producing captions and other outputs.	arXiv	2026.10	—
Multimodal CoBit	Multimodal Co-Generation With Continuous Bitstream Diffusion Reuses continuous bitstream diffusion from language modeling for multimodal co-generation, letting one checkpoint perform joint or conditional image–text and speech–text generation by choosing which bitstream parts are observed.	arXiv	2026.10
Modaliff	Modaliff: A Unified Token Diffusion Model for Any-to-Any Generation Assembles native text, image, and audio latent sequences into one token sequence with per-token attributes and role-based positional embeddings, so a single denoiser learns any-to-any generation from bimodal pairs.	arXiv	2026.10	—
JUICE ◆	JUICE: Unified Multimodal Modeling in Pretrained Representation Spaces Denoises frozen Flan-T5 text states and SigLIP2 image features in one flow-matching Transformer, trailing a matched autoregressive-text baseline on caption CIDEr (88.80 vs 160.52) at near-equal CLIPScore.	arXiv	2026.10
MF-1 ◆	Multimodal Flow: Unified Flow Modeling of Language and Vision in Embedding Spaces Organizes eight-token T5 text blocks and SigLIP2 image chunks into ordered continuous hyperchunks for one chunk-causal flow backbone, outscoring a matched autoregressive-text model on GQA, VQAv2, MMBench, and SEED-Bench.	arXiv	2026.09
BIT ◆	There and Back Again: Bidirectional Diffusion Bridges for Multimodality Translation Connects fixed token embeddings and image codes through a Brownian bridge, achieving lower image-to-text generative perplexity than its noise-started diffusion baseline while retaining comparable CLIP alignment to its deterministic-flow baseline.	arXiv	2026.08	—
GenFirst	GenFirst: Generation Before Reconstruction for Stable End-to-End Latent Generative Modeling Studies end-to-end training of a VAE and latent generative model, identifying the KL entropy term as essential against latent collapse and placing generation before reconstruction for stability.	arXiv	2026.08	—
ELF-S2T ◆	Speech Meets ELF: Audio Conditional Continuous-Target Diffusion for Speech Recognition and Translation Prepends projected Whisper features to noisy contextual text latents of a pretrained Embedded Language Flows model for speech-to-text, and audio forcing, which corrupts the text states used for decoder supervision, reduces transcription error.	arXiv	2026.06
MUNI	MUNI: Multimodal Unified Latent Diffusion for Coherent Any-to-Any Generation Trains latent diffusion end-to-end for any-to-any generation over a shared stochastic latent, from which a text decoder produces captions under subset conditioning or unconditional joint sampling.	NeurIPS 2026	2026.06	—
LipsFlow	A First Exploration of Neuromorphic OT-CFM for Multi-Speaker VSR Converts RGB videos into high-temporal-resolution event streams for multi-speaker visual speech recognition, using optimal-transport conditional flow matching to model the dense event features and speaker-specific articulation.	ECCV 2026	2026.06	—
DiffVC	DiffVC: A Non-autoregressive Framework Based on Diffusion Model for Video Captioning Generates video captions in parallel by denoising noised textual caption representations under encoded video features with a discriminative conditional diffusion model.	arXiv	2026.04	—
V-LCM	Unified Vision–Language Modeling via Concept Space Alignment Aligns visual inputs with the SONAR concept space and prepends visual vectors to the clean concept history, generating sentence-level concept vectors that a text decoder turns into text.	ICLR 2026	2026.03	—
ZS-DDAC	Zero-shot diverse audio captioning with diffusion models Brings diffusion-based diverse audio captioning to the zero-shot setting, sampling multiple distinct captions per audio clip.	Knowl.-Based Syst. 2026	2026	—
—	Exploring Unified Latent Diffusion for Multimodal Modeling Explores a unified latent diffusion approach to multimodal modeling in which text latents and other modality latents share one diffusion process.	ICLR 2027 submission	2026	—
FAC	Diverse and Few-Step Audio Captioning via Flow Matching Samples diverse audio captions in only a few steps by applying flow matching to caption generation conditioned on the audio clip.	ICASSP 2026	2026	—
CoUPLe	CoUPLe: Continuous Flow Unifying Pixels and Language Proposes a continuous flow model that unifies pixels and language, generating text and images within one shared process.	ICLR 2027 submission	2026	—
CoRe	CoRe: Jointly Learning Contextual Representations for Understanding and Generation Investigates jointly learned contextual representations that serve both understanding and generation, connecting text with visual or audio representations for multimodal modeling.	ICLR 2027 submission	2026	—
FlowBind ◆	FlowBind: Efficient Any-to-Any Generation with Bidirectional Flows Maps every observation to a shared anchor before following a single flow to sentence-level text vectors, improving CIDEr over OmniFlow in image and audio captioning, with higher CLIPScore for images but lower CLAPScore for audio.	ICLR 2026	2025.12	—
—	Diffusion Is Your Friend in Show, Suggest and Tell Feeds diffusion-generated caption suggestions into an autoregressive captioner instead of replacing it, combining bidirectional refinement with autoregressive structure and reaching 125.1 CIDEr-D on COCO without reinforcement learning.	IEEE BigData 2025	2025.12	—
Diffusion-Link	Diffusion-Link: Diffusion Probabilistic Model for Bridging the Audio-Text Modality Gap Carries audio embeddings from a frozen multimodal encoder into the text-embedding distribution with a lightweight diffusion module of three residual MLP blocks, narrowing the audio–text gap for LLM-based captioning.	ICASSP 2026	2025.10
IDMVAE	Disentanglement of Variations with Multimodal Generative Modeling Disentangles shared and modality-specific variation in a multimodal VAE with diffusion latent priors, decoding captions from the shared latent with a text decoder.	ICLR 2026	2025.09	—
ShaLa	ShaLa: Multimodal Shared Latent Generative Modelling Learns one shared latent variable for multimodal data and fits a second-stage conditional diffusion prior over it, so a text decoder can caption from generated shared latents.	AAAI 2026	2025.08	—
—	Non-autoregressive Modeling for Sign-gloss to Texts Translation Adapts DiffuSeq to sign-gloss-to-text translation, denoising continuous target-text embeddings conditioned on the gloss sequence as a non-autoregressive alternative to sequential decoding.	MT Summit 2025	2025.06	—
—	Image Captioning Based on Cross-Modal Cascaded Diffusion Model Cascades cross-modal diffusion stages for image captioning, progressively refining continuous caption states conditioned on visual features.	J. Zhejiang Univ. (Eng. Sci.) 2025	2025.04	—
FlowTok ◆	FlowTok: Flowing Seamlessly Across Text and Image Tokens Initializes the flow at encoded image latents and transports them directly into a compact text-token code, reporting 117.0 CIDEr on COCO Karpathy without CIDEr optimization.	ICCV 2025	2025.03
Diffusion-GDP	Generative Distribution Prediction: A Unified Approach to Multimodal Learning Frames multimodal learning as generative distribution prediction, diffusing sentence-level embeddings and decoding them back to text through iterative Vec2Text embedding inversion.	Machine Learning 2026	2025.02	—
PackDiT	PackDiT: Joint Human Motion and Text Generation via Mutual Prompting Links separate motion and text diffusion transformers through mutual blocks, so one model handles text-to-motion, motion-to-text, text generation, and joint motion–text generation.	arXiv	2025.01	—
UniTMGE	UniTMGE: Uniform Text-Motion Generation and Editing Model via Diffusion Unifies text–motion generation and editing in a shared-latent diffusion model paired with a text decoder.	WACV 2025	2025	—
POSCD-Net	Syntactic-Conditional Diffusion Networks for Controllable Image Captioning Conditions diffusion image captioning on syntactic skeletons as well as visual features, so the supplied syntax controls the structure of generated captions.	ACM TOMM 2025	2025	—
MirrorDiff	MirrorDiff: Learning Mirror Diffusion for Image Captioning via Regeneration Augments diffusion image captioning with a visual regeneration loss, refining continuous caption states under image features within a mirror-diffusion design.	ICMR 2025	2025	—
—	Interactive Image Caption Generation Reflecting User Intent from Trace Using a Diffusion Language Model Reflects user intent in image captions by conditioning a diffusion language model on user-provided traces, enabling interactive caption generation.	JACIII 2025	2025	—
DACRLD	Diffusion-based diverse audio captioning with retrieval-guided Langevin dynamics Steers a diffusion audio captioner with retrieval-guided Langevin dynamics during sampling, producing diverse captions for each audio clip.	Information Fusion 2025	2025	—
Diffusion Bridge	Diffusion Bridge: Leveraging Diffusion Model to Reduce the Modality Gap Between Text and Vision for Zero-Shot Image Captioning Bridges image embeddings toward the text-embedding space with a diffusion model, narrowing the vision–text modality gap for zero-shot image captioning.	CVPR 2025	2025
OmniFlow ◆	OmniFlow: Any-to-Any Generation with Multi-Modal Rectified Flows Couples text, image, and audio in one rectified-flow backbone, refining text codes jointly with the requested image or audio states through cross-modal attention while observed modalities stay clean.	CVPR 2025	2024.12
CrossFlow ◆	Flowing from Words to Pixels: A Noise-Free Framework for Cross-Modality Evolution Transports encoded image latents directly into a compressed text code with noise-free flow matching, reaching 116.2 COCO Karpathy CIDEr without CIDEr optimization and showing that training the image-to-text direction directly beats inverting a text-to-image flow.	CVPR 2025	2024.12
MM-Diff-Net	Diffusion-based Multimodal Video Captioning Extends diffusion-based caption generation to multimodal video input, denoising continuous caption states under temporal video streams.	ACCV 2024	2024.12	—
MoTe	MoTe: Learning Motion-Text Diffusion Model for Multiple Generation Tasks Learns marginal, conditional, and joint motion–text distributions with a diffusion model over latent embeddings from motion and text encoder-decoders, switching tasks such as motion captioning via input context.	arXiv	2024.11	—
DiffSLT ◆	DiffSLT: Enhancing Diversity in Sign Language Translation via Diffusion Model Translates sign language videos without glosses by diffusing a compact target-text latent under fused multi-level visual features and decoding it with a separate autoregressive decoder for diverse outputs.	Pattern Recognit. Lett. 2025	2024.11	—
DAC ◆	Towards Diverse and Efficient Audio Captioning via Diffusion Models Targets diverse, efficient audio captioning by diffusing full-length contextual text states under audio conditioning and decoding them with a separate parallel decoder.	Interspeech 2025	2024.09	—
Diff-MVAE	Multimodal ELBO with Diffusion Decoders Adds diffusion decoders for complex modalities to the multimodal VAE ELBO and an auxiliary score-based prior over the shared latent, from which a text decoder produces captions.	CVPR 2026 Workshops	2024.08	—
LaDiC ◆	LaDiC: Are Diffusion Models Really Inferior to Autoregressive Counterparts for Image-to-Text Generation? Diffuses token-aligned contextual BERT states under image features, trailing BLIP CapFilt-L on COCO CIDEr (126.2 vs 133.3) but exceeding fine-tuned BLIP-base on Stanford paragraph captioning (7.3 vs 6.1 BLEU-4).	NAACL 2024	2024.04
DiffuVST	DiffuVST: Narrating Fictional Scenes with Global-History-Guided Denoising Models Narrates sequences of fictional scenes as visual stories with a denoising diffusion model guided by global history, adapting diffusion text generation to image sequences.	Findings of EMNLP 2023	2023.12	—
C3Net	C3Net: Compound Conditioned ControlNet for Multimodal Content Generation Combines conditions from several modalities through a ControlNet-style compound-conditioning design, connecting text with visual or audio representations for multimodal content generation.	CVPR 2024	2023.11	—
EasyGen	EasyGen: Easing Multimodal Generation with BiDiffuser and LLMs Pairs the BiDiffuser diffusion model with large language models through a BiDiffuser-to-LLM projection to connect text and visual representations for multimodal generation.	ACL 2024	2023.10
Prefix-diffusion	Prefix-diffusion: A Lightweight Diffusion Model for Diverse Image Captioning Builds a lightweight diffusion captioner that refines continuous token embeddings under prefix image features, targeting diverse image captions.	LREC-COLING 2024	2023.09
LAM-MSC	Large AI Model Empowered Multimodal Semantic Communications Routes multimodal semantic communication through a CoDi-based multimodal alignment module whose composable diffusion converts between modalities and text, aided by a personalized LLM knowledge base.	IEEE Commun. Mag. 2025	2023.09	—
MLD	Multi-Modal Latent Diffusion Concatenates latents from independently trained unimodal deterministic autoencoders into a shared space and co-denoises them, text included, with a masked score-based diffusion model using multi-time training.	Entropy 2024	2023.06
DiffCap ◆	DiffCap: Exploring Continuous Diffusion on Image Captioning Transforms caption tokens into learned continuous embeddings and diffuses them while fusing extracted image features, performing comparably to earlier non-autoregressive captioners on COCO with a simpler structure.	arXiv	2023.05
UniDiffuser ◆	One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale Co-denoises images and low-dimensional text codes in one transformer that covers image captioning and text-to-image generation, with a separate autoregressive decoder mapping text codes to captions.	ICML 2023	2023.03
SCD-Net ◆	Semantic-Conditional Diffusion Networks for Image Captioning Encodes captions as analog bits and diffuses them under visual features and semantic conditions, reporting 118.0 CIDEr on COCO Karpathy test without CIDEr optimization.	CVPR 2023	2022.12
CLIP-Diffusion-LM	CLIP-Diffusion-LM: Apply Diffusion Model on Image Captioning Applies denoising diffusion probabilistic models to caption token embeddings under CLIP image features, reaching 0.2470 BLEU-4 when trained on combined Flickr8k and Flickr30k data.	arXiv	2022.10

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Dialogue and Discourse Planning

Dialogue, empathy, and discourse systems that plan with utterance- or paragraph-level latent vectors. _{(Survey §6.1.4, App. G.4)}

Model	Paper	Venue	Date	Code
—	Reason Before You Speak with Latent Diffusion Integrates a latent diffusion planner into an autoregressive backbone, refining a plan-level latent vector that then conditions autoregressive realization of the response.	ICLR 2027 submission	2026	—
DEDM	Modeling Latent Background Information in Multiturn Dialogues Using Diffusion Model Models latent background information in multi-turn dialogues with a diffusion prior over background-factor latents that condition autoregressive response generation.	IEEE TAI 2026	2026	—
LisenDiff	Facilitating Cross-lingual Transfer of Empathy through Language-independent Latent Diffusion: A Case Study in Chinese Transfers empathy cross-lingually to Chinese through language-independent latent diffusion, whose diffused latent vectors condition autoregressive generation of empathetic responses.	Findings of EMNLP 2025	2025.11
DiffusionDialog ◆	DiffusionDialog: A Diffusion Model for Diverse Dialog Generation with Latent Space Diversifies dialogue responses by drawing a continuous response latent from a Gaussian diffusion prior and realizing it with a separate autoregressive decoder.	LREC-COLING 2024	2024.04	—
Diffuse-CG	Controllable Conversation Generation with Conversation Structures via Diffusion Models Edits prototype dialogues with a diffusion model conditioned on conversation structures to generate controllable conversations.	Findings of ACL 2023	2023.07	—
DiffusEmp	DiffusEmp: A Diffusion Model-Based Framework with Multi-Grained Control for Empathetic Response Generation Produces empathetic dialogue responses with a diffusion generator under multi-grained control signals, including empathy and intent cues.	ACL 2023	2023.06	—
Dior-CVAE ◆	Dior-CVAE: Pre-trained Language Models and Diffusion Priors for Variational Dialog Generation Builds a hierarchical variational dialogue model on pretrained language models with a Gaussian diffusion prior over utterance-level latents that condition a separate autoregressive decoder.	Findings of EMNLP 2023	2023.05

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Code, Structured Outputs, and Synthetic Data

Code generation, structured outputs, symbolic expressions, and synthetic or private training corpora. _{(Survey §6.1.5, App. G.5)}

Model	Paper	Venue	Date	Code
DiffuSR	Discovering Mathematical Equations with Diffusion Language Model Tackles symbolic regression by denoising embedded mathematical-symbol sequences with a continuous-state diffusion language model that cross-attends to numerical data and supplies expression priors.	arXiv	2025.09	—
DDPT	DDPT: Diffusion-Driven Prompt Tuning for Large Language Model Code Generation Automates prompt engineering for LLM code generation by denoising Gaussian noise into soft prompt embeddings for a frozen code model, trained with that model's code generation loss.	CAIN 2025	2025.04	—
CoDSA	Conditional Data Synthesis Augmentation Fills under-sampled regions of multimodal training data with conditional synthetic examples, producing text by diffusing sentence embeddings and decoding them via iterative Vec2Text inversion.	JASA 2026	2025.04	—
CDA²	CDA²: Counterfactual Diffusion Augmentation for Cross-Domain Adaptation in Low-Resource Sentiment Analysis Augments low-resource cross-domain sentiment analysis with diffusion-generated counterfactual text, where continuous rewriting with sentence-level target-domain alignment beats word-substitution baselines and its filtered variant matches UDALM's average accuracy across twelve Amazon domain-transfer tasks.	COLING 2025	2025	—
DiffLM ◆	DiffLM: Controllable Synthetic Data Generation via Diffusion Language Models Produces controllable synthetic data by diffusing sentence-level latent vectors that a separate autoregressive decoder reads out, with GPT-4 and human evaluators favoring individual generated tool descriptions while GPT-4 prefers real tool collections at the category level.	Findings of ACL 2025	2024.11
—	Private Synthetic Text Generation with Diffusion Models Trains continuous text diffusion models with DP-SGD to generate differentially private synthetic corpora for training downstream models.	NAACL 2025	2024.10	—
DiffusPoll	DiffusPoll: Conditional Text Diffusion Model for Poll Generation Generates structured poll questions together with their options using a conditional text diffusion model that denoises continuous representations.	Findings of ACL 2024	2024.08	—
—	Improving aggressiveness detection using a data augmentation technique based on a Diffusion Language Model Enlarges aggressiveness-detection training sets with synthetic text sampled from a continuous diffusion language model, providing data augmentation for abuse-detection classifiers.	WOAH 2024	2024	—
DCA	Diffusion Based Counterfactual Augmentation for Dual Sentiment Classification Flips sentiment labels via diffusion-generated antonymous rewrites for dual sentiment classification, with modest gains over lexical substitution and much larger losses when candidate-word selection or the dual sentiment classifier is removed.	LREC-COLING 2024	2024	—
CodeFusion ◆	CodeFusion: A Pre-trained Diffusion Model for Code Generation Pretrains a 75M Gaussian embedding diffusion model with a separate contextual decoder for natural-language-to-code, staying close to CodeT5 and GPT-3 at top-1 and exceeding them with top-5 candidate pools.	EMNLP 2023	2023.10	—

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Reasoning, Knowledge, and Instruction Following

Math and commonsense reasoning, latent thought trajectories, reinforcement-learning post-training, retrieval- and knowledge-grounded generation, and instruction following. _{(Survey §6.1.6, App. G.6)}

Model	Paper	Venue	Date	Code
GRADi4GCR	An Empirical Study of Retrieval-Augmented Diffusion Language Models for Generative Commonsense Reasoning Evaluates retrieval-augmented diffusion language models on generative commonsense reasoning in an empirical study of knowledge-intensive diffusion text generation.	Information Sciences 2027	2027	—
FLaRe	What Matters for Latent Reasoning with Flow Matching Defines five requirements for latent thoughts, including diversity, explainability, and refinability, and identifies training choices that make learned-latent flow matching work for LLM reasoning.	arXiv	2026.10	—
Unrolled Flow Models	Unrolled Flow Models for Reasoning Optimizes an endpoint loss through unrolled latent flow updates, with truncated backpropagation for longer rollouts, enabling test-time compute scaling on synthetic reasoning where standard per-step flow matching plateaus.	arXiv	2026.10	—
ReasonFlow	ReasonFlow: Flow Matching that Thinks Step by Step Builds step-by-step thinking into flow matching through intermediate chain-of-thought anchor supervision for multi-step latent reasoning.	Findings of EMNLP 2026	2026.10
RDD	Rationale Distribution Distillation via Flow Matching for Distributional Continuous Latent Reasoning Distills multiple textual reasoning paths into a conditional flow that non-autoregressively samples fixed-length latent rationales, from which a frozen language model decodes answers.	arXiv	2026.10	—
Sigma ◆	Large Language Continuous Diffusion Models Scales likelihood-trained embedding diffusion to 3B and 8B by blockwise adaptation of autoregressive checkpoints, closely matching compute-matched masked diffusion and its autoregressive initializations on math and code benchmarks.	arXiv	2026.10	—
—	Efficient Reasoning with Flow Language Models Studies flow language models on Sudoku and maze search, showing that a Sudoku state decomposes into residual initial noise plus a weighted history of clean predictions and that restricting locally feasible digits reduces subsequent recovery.	arXiv	2026.10	—
SkillFM	SkillFM: Generating Skills for LLM Agents via Latent Flow Matching Synthesizes task-conditioned textual skills for LLM agents by sampling a codec latent in one step with a MeanFlow-trained conditional flow and decoding it with an LLM.	arXiv	2026.09
CEDR ◆	Reasoning with Continuous Latent Diffusion Trains an ELF-based flow on learned multi-layer projections of an instruction-tuned teacher's states, showing that a highly decodable single-layer target reasons poorly while spreading the representation across layers markedly improves math reasoning.	arXiv	2026.09
ATF	Next Thoughts Are Distributions: Generative Autoregressive Reasoning in the Latent Space Models each next continuous thought as a multimodal distribution sampled by a lightweight diffusion head atop a causal autoregressive model, feeding sampled thoughts back for variable-length latent reasoning.	arXiv	2026.09	—
ELF-REG ◆	ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks Extends Embedded Language Flows to math reasoning and code by aligning denoiser features with a frozen autoregressive teacher whose global representation is denoised jointly with the response.	arXiv	2026.09
Evo	Evo: Autoregressive–Diffusion Large Language Models with Evolving Balance Evolves each token embedding along its own progression variable within a shared probability flow, balancing autoregressive-like refinement and diffusion-style planning by uncertainty, trained with a unified variational ELBO.	EMNLP 2026	2026.03	—
LaDi-RL	LaDi-RL: Latent Diffusion Reasoning Prevents Entropy Collapse in Reinforcement Learning Optimizes a latent diffusion policy over reasoning trajectories with GRPO to counter entropy collapse, sampling several answer realizations per latent trajectory to separate plan failures from realization failures.	arXiv	2026.02	—
—	Tilted Generator Matching: One RL Objective For Every Diffusion and Flow Model Formulates tilted generator matching, one reinforcement-learning objective proposed to cover every diffusion and flow model, for reward-based post-training.	ICLR 2027 submission	2026	—
BioNGen	Semantic Knowledge Guided Diffusion Model for Biomedical Ontology Definition Generation Generates definitions for biomedical ontology concepts with a diffusion model guided by semantic knowledge, extending text diffusion to knowledge-intensive concept-to-text generation.	JHIR 2026	2026	—
RaDi4GCR	Retrieval-Augmented Diffusion Language Model for Generative Commonsense Reasoning Equips a diffusion language model with retrieval augmentation for generative commonsense reasoning, extending text diffusion to knowledge-intensive generation.	DASFAA 2026	2026	—
ReLPO	ReLPO: Resolution-Lifted Policy Optimization for Autoregressive–Diffusion Language Models Introduces resolution-lifted policy optimization, a reinforcement-learning post-training scheme for language models that combine autoregressive and diffusion generation.	ICLR 2027 submission	2026	—
LaDi-OPSD	Reinforcing LLM Latent Reasoning with Contextual Loops through On-Policy Flow-Map Self-Distillation Reinforces LLM latent reasoning through on-policy flow-map self-distillation with contextual loops.	ICLR 2027 submission	2026	—
SC-dLLM	Into the Continuum: Efficient Semi-Continuous Diffusion LLMs Converts a pretrained autoregressive model into a blockwise semi-continuous diffusion LLM with a small additional token budget, targeting efficient generation.	ICLR 2027 submission	2026	—
TESS 2 ◆	TESS 2: A Large-Scale Generalist Diffusion Language Model Adapts a pretrained autoregressive backbone into a simplex-state Gaussian diffusion model for instruction following, using continued pretraining, instruction tuning, and inference-time reward guidance.	ACL 2025	2025.02
ASSIGNER	Retrieval Augmented Encoder-Decoder with Diffusion for Sequential Hashtag Recommendation in Disaster Events Recommends hashtag sequences during disaster events by pairing a retrieval-augmented encoder-decoder with diffusion, framing sequential hashtag recommendation as sequence generation.	ICWSM 2025	2025	—
DoT ◆	Diffusion of Thought: Chain-of-Thought Reasoning in Diffusion Language Models Brings chain-of-thought to embedding diffusion by anchoring problem tokens and denoising rationale and answer embeddings, either jointly in one pass or rationale by rationale across passes.	NeurIPS 2024	2024.02
DiffuCOMET ◆	DiffuCOMET: Contextual Commonsense Knowledge Diffusion Jointly denoises sets of compressed fact vectors for contextual commonsense inference, producing more diverse and contextually relevant knowledge clusters than beam-search baselines while trading relevance for diversity as refinement steps increase.	ACL 2024	2024.02

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Scientific and Domain Applications

Remote-sensing change captioning, molecular and 3D-shape captioning, radiology report generation, and brain-signal decoding. _{(Survey App. G.7)}

Model	Paper	Venue	Date	Code
BiMol-Diff	BiMol-Diff: A Unified Diffusion Framework for Molecular Generation and Captioning Unifies molecule generation and difficulty-scheduled molecular captioning in one diffusion framework, but its higher-quality sampling runs slower than autoregressive baselines and fewer refinement steps erase its quality margin.	ACL 2026	2026.04	—
Diff-3DCap	Diff-3DCap: Shape Captioning with Diffusion Models Represents 3D objects as sequences of projected views and captions them by denoising Gaussian-perturbed caption embeddings with a continuous diffusion model conditioned on pretrained visual embeddings.	IEEE TVCG 2025	2025.09	—
CoDiXR	Any-to-Any Vision-Language Model for Multimodal X-ray Imaging and Radiological Report Generation Synthesizes multi-view chest X-rays and associated radiology reports with an any-to-any diffusion framework built on MIMIC-CXR, scored by FID for images and BLEU for text.	IJCNN 2025	2025.05	—
XGeM	XGeM: A Multi-Prompt Foundation Model for Multimodal Medical Data Generation Supports any-to-any diffusion-based synthesis across medical data modalities, including radiology reports, with a 6.77B-parameter model combining a contrastive shared latent space and multi-prompt training on arbitrary input subsets.	CMIG 2026	2025.01	—
Diffusion-RSCC	Diffusion-RSCC: Diffusion Probabilistic Model for Change Captioning in Remote Sensing Images Captions semantic changes between bi-temporal remote-sensing image pairs by denoising caption representations from Gaussian noise with a noise predictor conditioned on cross-modal features.	IEEE TGRS 2025	2024.05
MedM2G	MedM2G: Unifying Medical Multi-Modal Generation via Cross-Guided Diffusion with Visual Invariant Integrates radiology report generation into a unified medical multimodal cross-guided diffusion model that aligns modalities in a shared space while preserving each imaging modality's visual invariant.	CVPR 2024	2024.03	—
UniBrain	UniBrain: Unify Image Reconstruction and Captioning All in One Diffusion Model from Human Brain Activity Decodes visually evoked fMRI into captions and reconstructed images with one latent diffusion model, mapping voxels to text and image latents and guiding denoising with fMRI-derived conditions.	arXiv	2023.08	—

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📊 Evaluation, Analysis, and Theory

Evaluation measures and likelihood estimators, benchmarks and diagnostics, interpretability of generation dynamics, and theory of continuous text generators. _{(Survey §6.2–§7, App. B, D)}

Model	Paper	Venue	Date	Code
SOL	SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics Quantifies gaps between text distributions for evaluating diffusion and flow language models, comparing per-sequence hidden-state measures under a fixed transformer with a double sliced Wasserstein distance.	arXiv	2026.10	—
—	Parallelism, critical windows, and separations among diffusion language models Proves that Gaussian diffusion on one-hot encodings can sample in forward passes scaling with dual total correlation, tracing its separation from masked diffusion to a wider critical noise window.	arXiv	2026.09	—
—	Hacking Generative Perplexity: Why Unconditional Text Evaluation Needs Distributional Metrics Constructs training-free samplers whose periodic, incoherent text reaches low GenPPL at non-degenerate unigram entropy yet fails distributional checks, and rebenchmarks diffusion language models with distributional metrics.	ICML 2026 Workshop	2026.06
—	When Latent Geometry Is Not Enough: Draft-Conditioned Latent Refinement for Non-Autoregressive Text Generation Finds that generated latents near frozen BERT encoder states can still decode to high-entropy or repetitive text, and reframes generation as draft-conditioned, flow-based local latent refinement.	arXiv	2026.05
DiffuTruth	The Energy of Falsehood: Detecting Hallucinations via Diffusion Model Likelihoods Detects hallucinations by noising and reconstructing a claim's embeddings with a diffusion model, converting reconstruction stability into a factuality score via an external natural-language-inference model.	FEVER 2026	2026.02	—
—	The Truncation Trap: Silent Failure of Fixed-Window Diffusion Likelihood and Information Estimators under Representation Drift Shows that fixed log-SNR windows with stale scale-dependent tail corrections can omit mass from direct denoising-error integrals under representation drift and lose the full-line entropy upper-bound guarantee, whereas finite-window variational bounds with live endpoint terms keep their bound.	ICLR 2027 submission	2026	—
—	The Generative Gap Between Speculative Drafter and Continuous Diffusion Language Model Compares the continuous diffusion language model LangFlow with standalone DSpark drafter adaptations in standalone generation to characterize the generative gap between the two approaches.	ICLR 2027 submission	2026	—
FlowScope	FlowScope: Interpreting Generation Dynamics in Continuous Flow Language Models Interprets generation dynamics in continuous flow language models by tracing how intermediate states evolve, informing inference-time choices such as step allocation and halting.	ICLR 2027 submission	2026	—
FATE	Faster Density Estimation and Inference-Time Steering for Flow Language Models Accelerates density estimation for flow language models with a denoiser-based estimator that scores density without explicit divergence computation, and adds inference-time steering of their sampling.	NeurIPS 2026 Workshop	2026	—
—	Explore, Revisit, or Commit: Prediction Dynamics in Continuous Diffusion Language Models Analyzes how positions explore, revisit, or commit during continuous diffusion language model sampling, showing that freezing surrounding prediction memory alters local revision dynamics.	ICLR 2027 submission	2026	—
DistillScope	DistillScope: Benchmarking Flow-Map Distillation for Language Generation Benchmarks flow-map distillation recipes for language generation within one framework, studying how perplexity, MAUVE, training-time accounting, and inference budget change their rankings.	ICLR 2027 submission	2026	—
—	Perfect diffusion is TC⁰ – Bad diffusion is Turing-complete Establishes a complexity dichotomy for diffusion language modeling, showing exact score networks stay within TC0 while networks unconstrained by any score function can simulate any Turing machine.	arXiv	2025.07	—
—	How Does Diffusion Influence Pretrained Language Models on Out-of-Distribution Data? Probes diffusion-adapted RoBERTa on out-of-distribution data, using reconstruction error under fixed corruption to detect out-of-domain inputs and finding longer training lowers reconstruction loss but raises generated-text perplexity.	ECAI 2023	2023.07	—

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🗺️ Core Systems at a Glance

The survey's method lookup table (Appendix F) lists 133 core systems once each, with four standardized attributes: the continuous state, the training target, the transition and generation order, and the decoder. It is reproduced, with links, in docs/core-systems.md.

🔗 Related Awesome Lists

These lists cover neighboring ground, mostly discrete and masked diffusion language models, which this list leaves out on purpose:

• Awesome-DLMs - Companion list of "A Survey on Diffusion Language Models", covering discrete, continuous, and multimodal diffusion language models.
• DLLM-Survey - Companion list of "Discrete Diffusion in Large Language and Multimodal Models: A Survey" (TMLR 2026).
• Awesome Discrete Diffusion Models - Papers and resources on discrete diffusion models.
• Diffusion-LLM-Papers - A collection of papers on diffusion language models.
• Awesome-Parallel-Text-Generation - Companion list of "A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Models".
• Awesome-Text-Diffusion-Models - Companion list of "Diffusion Models for Non-autoregressive Text Generation: A Survey" (IJCAI 2023).
• diffusion-nlp-paper-arxiv - An automatically updated feed of arXiv papers on diffusion models for NLP.
• Awesome-Diffusion-Models - Resources and papers on diffusion models across modalities.

🤝 Contributing

Missing a paper, or spotted a wrong link, venue, or summary? Please open an issue or send a pull request. The list is generated from data/papers.yaml, so a new entry is a few lines of YAML; see CONTRIBUTING.md. The scope is strictly continuous: models that generate text or code by transforming real-valued representations through diffusion, flow, flow-map, or drifting updates, and studies of such models.

📝 Citation

If you find the survey or this list useful, please cite:

@misc{tokenrhythm2026cdllm,
  title        = {Continuous-Space Diffusion and Flow Language Models: A Survey},
  author       = {{TokenRhythm Technologies}},
  year         = {2026},
  url          = {https://github.com/TokenRhythm/awesome-cdllm}
}

---

_{Maintained by TokenRhythm Technologies · literature coverage through 24 October 2026.}