diff --git a/unit1/01_introduction_to_diffusers.ipynb b/unit1/01_introduction_to_diffusers.ipynb
index ba1bf2b..5c3aa19 100644
--- a/unit1/01_introduction_to_diffusers.ipynb
+++ b/unit1/01_introduction_to_diffusers.ipynb
@@ -692,7 +692,7 @@
"q(\\mathbf{x}_{1:T} \\vert \\mathbf{x}_0) = \\prod^T_{t=1} q(\\mathbf{x}_t \\vert \\mathbf{x}_{t-1})$
\n",
"\n",
"\n",
- "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\beta_t$. This $\\beta$ is defined for every t according to some schedule, and determines how much noise is added per timestep. Now, we don't necessarily want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$:
\n",
+ "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\sqrt{\\beta_t}$. This $\\beta$ is defined for every t according to some schedule, and determines how much noise is added per timestep. Now, we don't necessarily want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$:
\n",
"\n",
"$\\begin{aligned}\n",
"q(\\mathbf{x}_t \\vert \\mathbf{x}_0) &= \\mathcal{N}(\\mathbf{x}_t; \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0, {(1 - \\bar{\\alpha}_t)} \\mathbf{I})\n",
diff --git a/unit1/02_diffusion_models_from_scratch.ipynb b/unit1/02_diffusion_models_from_scratch.ipynb
index 70b3c94..38f687b 100644
--- a/unit1/02_diffusion_models_from_scratch.ipynb
+++ b/unit1/02_diffusion_models_from_scratch.ipynb
@@ -1484,10 +1484,10 @@
"q(\\mathbf{x}_{1:T} \\vert \\mathbf{x}_0) = \\prod^T_{t=1} q(\\mathbf{x}_t \\vert \\mathbf{x}_{t-1})$
\n",
"\n",
"\n",
- "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\beta_t$. This $\\beta$ is defined for every t according to some schedule, and determines how much noise is added per timestep. Now, we don't necessarily want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$:
\n",
+ "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\sqrt{\\beta_t}$. This $\\beta$ is defined for every t according to some schedule, and determines how much noise is added per timestep. Now, we don't necessarily want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$:
\n",
"\n",
"$\\begin{aligned}\n",
- "q(\\mathbf{x}_t \\vert \\mathbf{x}_0) &= \\mathcal{N}(\\mathbf{x}_t; \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0, \\sqrt{(1 - \\bar{\\alpha}_t)} \\mathbf{I})\n",
+ "q(\\mathbf{x}_t \\vert \\mathbf{x}_0) &= \\mathcal{N}(\\mathbf{x}_t; \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0, {(1 - \\bar{\\alpha}_t)} \\mathbf{I})\n",
"\\end{aligned}$ where $\\bar{\\alpha}_t = \\prod_{i=1}^T \\alpha_i$ and $\\alpha_i = 1-\\beta_i$
\n",
"\n",
"The maths notation always looks scary! Luckily the scheduler handles all that for us (uncomment the next cell to check out the code). We can plot $\\sqrt{\\bar{\\alpha}_t}$ (labelled as `sqrt_alpha_prod`) and $\\sqrt{(1 - \\bar{\\alpha}_t)}$ (labelled as `sqrt_one_minus_alpha_prod`) to view how the input (x) and the noise are scaled and mixed across different timesteps:\n"