Diffusion Path Samplers via Sequential Monte Carlo

We develop a diffusion-based sampler for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a (simple) base distribution and the target distribution, widely used in diffusion models. Our approach is based on a practical implementation of diffusion-annealed Langevin Monte Carlo, which approximates the diffusion path with convergence guarantees. We tackle the score estimation problem by developing an efficient sequential Monte Carlo sampler that evolves auxiliary variables from conditional distributions along the path, which provides principled score estimates for time-varying distributions. We further develop novel control variate schedules that minimise the variance of these score estimates. Finally, we provide theoretical guarantees and empirically demonstrate the effectiveness of our method on several synthetic and real-world datasets.

On Diffusion Posterior Sampling via Sequential Monte Carlo for Zero-Shot Scaffolding of Protein Motifs

With the advent of diffusion models, new proteins can be generated at an unprecedented rate. The \textit{motif scaffolding problem} requires steering this generative process to yield proteins with a desirable functional substructure -- a motif. While models have been trained to take the motif as conditional input, recent techniques in diffusion posterior sampling can be leveraged as zero-shot alternatives whose approximations can be corrected with sequential Monte Carlo (SMC) algorithms. In this work, we introduce a new set of guidance potentials to describe and solve scaffolding tasks by adapting SMC-aided diffusion posterior samplers with an unconditional model, Genie, acting as a prior. Against established benchmarks, we successfully scaffold several single-motif and multi-motif problems. The latter is possible by pairing reconstruction guidance with $\mathrm{SE}(3)$-invariant potentials. In the single-motif case, we find these potentials perform comparably to the conventional masking approach and that reconstruction guidance outperforms replacement methods when aided with SMC. We additionally consider a guidance potential for point symmetry constraints and produce designable internally symmetric monomers with our setup. Overall, this work highlights the capabilities and areas for improvement of zero-shot posterior samplers in motif scaffolding tasks. Code is available at: https://github.com/matsagad/mres-project