diff --git a/docs/diffusion/ddpm/index.html b/docs/diffusion/ddpm/index.html
index 13670185..da0dba1b 100644
--- a/docs/diffusion/ddpm/index.html
+++ b/docs/diffusion/ddpm/index.html
@@ -102,7 +102,7 @@ c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z">x0,(1−αtˉ)I)where αt=1−βt and αtˉ=∏s=1tαs
Reverse Process
The reverse process removes noise starting at p(xT)=N(xT;0,I) for T time steps.
-pθ(xt−1∣xt)pθ(x0:T)pθ(x0)=N(xt−1;μθxt,t),Σθ(xt,t))=pθ(xT)t=1∏Tpθ(xt−1∣xt)=∫pθ(x0:T)dx1:Tθ are the parameters we train.
+pθ(xt−1∣xt)pθ(x0:T)pθ(x0)=N(xt−1;μθ(xt,t),Σθ(xt,t))=pθ(xT)t=1∏Tpθ(xt−1∣xt)=∫pθ(x0:T)dx1:Tθ are the parameters we train.
Loss
We optimize the ELBO (from Jenson's inequality) on the negative log likelihood.
E[−logpθ(x0)]≤Eq[−logq(x1:T∣x0)pθ(x0:T)]=LThe loss can be rewritten as follows.
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index 1869b1d7..e0cbfaa6 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -561,7 +561,7 @@
https://nn.labml.ai/transformers/models.html
- 2022-06-28T16:30:00+00:00
+ 2022-07-02T16:30:00+00:00
1.00
@@ -652,7 +652,7 @@
https://nn.labml.ai/transformers/basic/autoregressive_experiment.html
- 2022-06-28T16:30:00+00:00
+ 2022-07-02T16:30:00+00:00
1.00
@@ -813,7 +813,7 @@
https://nn.labml.ai/transformers/positional_encoding.html
- 2021-10-21T16:30:00+00:00
+ 2022-07-02T16:30:00+00:00
1.00
@@ -855,7 +855,7 @@
https://nn.labml.ai/transformers/mha.html
- 2022-06-28T16:30:00+00:00
+ 2022-07-02T16:30:00+00:00
1.00
diff --git a/labml_nn/diffusion/ddpm/__init__.py b/labml_nn/diffusion/ddpm/__init__.py
index e4fc9684..228b494c 100644
--- a/labml_nn/diffusion/ddpm/__init__.py
+++ b/labml_nn/diffusion/ddpm/__init__.py
@@ -47,7 +47,7 @@ for $T$ time steps.
\begin{align}
\textcolor{lightgreen}{p_\theta}(x_{t-1} | x_t) &= \mathcal{N}\big(x_{t-1};
- \textcolor{lightgreen}{\mu_\theta}x_t, t), \textcolor{lightgreen}{\Sigma_\theta}(x_t, t)\big) \\
+ \textcolor{lightgreen}{\mu_\theta}(x_t, t), \textcolor{lightgreen}{\Sigma_\theta}(x_t, t)\big) \\
\textcolor{lightgreen}{p_\theta}(x_{0:T}) &= \textcolor{lightgreen}{p_\theta}(x_T) \prod_{t = 1}^{T} \textcolor{lightgreen}{p_\theta}(x_{t-1} | x_t) \\
\textcolor{lightgreen}{p_\theta}(x_0) &= \int \textcolor{lightgreen}{p_\theta}(x_{0:T}) dx_{1:T}
\end{align}