A framework for conditional diffusion modelling with applications in motif scaffolding for protein design (2312.09236v4)

Abstract: Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods.

• The paper presents a novel conditional diffusion framework using Doob's h-transform to improve motif scaffolding in protein design.
• It introduces an innovative amortised training process that refines both training and sampling protocols in diffusion models.
• Empirical results demonstrate superior performance compared to standard methods in both image generation and protein motif scaffolding.

Introduction

Generative models have been prominently featured in various design applications. Denoising diffusion models are among the most effective generative tools, with capabilities that extend from creating high-quality images to aiding in the complex process of protein design. In protein design, a critical aspect is the incorporation of a structural motif—a pattern of amino acids responsible for a protein's function—into a protein’s structure. This must be skillfully done such that the designed proteins can fold correctly and remain stable.

Framework Overview

This paper presents a comprehensive framework for conditional diffusion modelling based on Doob's h-transform. This mathematical tool provides a coherent basis for conditioning stochastic processes, which is central to generative modelling, especially when dealing with protein motifs. The framework integrates both the training procedures and the sampling protocols underpinning generative diffusion models, connecting existing methods and explicating their commonalities and differences.

The research reveals a gap in the current literature by highlighting the absence of specific methods within the established range of conditioning techniques. To fill this gap, a novel approach, termed amortised training, is proposed.

Empirical Examination

The utility of the proposed framework is not merely theoretical. The authors extend the framework's practicality by applying it to concrete problems, starting with image generation and then tackling the more complex motif scaffolding issue in protein design. Experiments leverage a diffusion model to generate image outpaintings and scaffold motifs for protein design, with a focus on outlining the merits and potential drawbacks of the new amortised training approach.

The results showcase the effectiveness of the amortised training method, affirming its potential by outstripping standard methods in motif scaffolding tasks. Moreover, the approach has been empirically evaluated against other methods in terms of both image and protein design, where the novel amortised training approach shows promising results.

Contributions and Implications

The paper contributes to the research community on several fronts: it provides a formal framework for conditional diffusion processes, classifies existing methods, introduces a new and effective approach to conditional training, and empirically verifies various approaches in practical tasks. Notably, archived plug-and-play algorithms for different conditioning schemes support potential future adaptations.

Such advancements could have implications for drug discovery and the creation of novel enzymes, where precise protein design is a prerequisite. The method's potential to streamline and enhance the motif scaffolding process may translate into significant strides in protein engineering.