Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem

[bd3dowling]

Trippe, Brian L., et al. Diffusion Probabilistic Modeling of Protein Backbones in 3D for the Motif-Scaffolding Problem. arXiv:2206.04119, arXiv, 19 Mar. 2023. arXiv.org, http://arxiv.org/abs/2206.04119.

[bd3dowling]

Paste from obsidian:

• Quite technical on the protein / biology side.
• Develops SMCDiff for conditional sampling from their ProtDiff model.
• Key is that assumes the $p_{\theta}$ accurately approximates $q$.
• Also, only applies to in-painting (have true values at certain dimension indices).

\begin{algorithm}
\caption{SMCDiff: Particle Filtering for Conditionally Sampling from Unconditional Diffusion Models}
\begin{algorithmic}
\State \textbf{Input:} $x^{(0)}_M$ (motif), $K$ (\# of particles)

\State \Comment{Forward diffuse motif}
\State $\hat{x}_{1:T}^M \sim q(x_{1:T}^M \mid x^{(0)}_M)$

\State \Comment{Reverse diffuse particles}
\ForAll{$k$}
    \State $x^{(T)}_k \sim p_\theta(x^{(T)})$
\EndFor

\For{$t \gets T$ to $1$}
    \State \Comment{Replace motif}
    \ForAll{$k$}
        \State $x^{(t)}_k \leftarrow [\hat{x}^{(t)}_M, x^{(t)}_{S,k}]$ \Comment{Concatenate motif with state}
    \EndFor

    \State \Comment{Re-weight based on previous motif}
    \ForAll{$k$}
        \State $w^{(t)}_k \leftarrow p_\theta(\hat{x}^{(t-1)}_M \mid x^{(t)}_k)$
    \EndFor
    \ForAll{$k$}
        \State $\tilde{w}^{(t)}_k \leftarrow \frac{w^{(t)}_k}{\sum_{k'=1}^K w^{(t)}_{k'}}$
    \EndFor

    \State $\tilde{x}^{(t)}_{1:K} \sim \text{Resample}(\tilde{w}^{(t)}_{1:K}, x^{(t)}_{1:K})$

    \State \Comment{Propose next step}
    \ForAll{$k$}
        \State $x^{(t-1)}_k \sim p_\theta(x^{(t-1)} \mid \tilde{x}^{(t)}_k)$
    \EndFor
\EndFor
\Output $x^{(0)}_{S,1:K}$
\end{algorithmic}
\end{algorithm}

[bd3dowling]

Pretty challenging paper to follow...