Diffusion Models for Constrained Domains

Denoising diffusion models are a recent class of generative models which achieve state-of-the-art results in many domains such as unconditional image generation and text-to-speech tasks. They consist of a noising process destroying the data and a backward stage defined as the time-reversal of the noising diffusion. Building on their success, diffusion models have recently been extended to the Riemannian manifold setting. Yet, these Riemannian diffusion models require geodesics to be defined for all times. While this setting encompasses many important applications, it does not include manifolds defined via a set of inequality constraints, which are ubiquitous in many scientific domains such as robotics and protein design. In this work, we introduce two methods to bridge this gap. First, we design a noising process based on the logarithmic barrier metric induced by the inequality constraints. Second, we introduce a noising process based on the reflected Brownian motion. As existing diffusion model techniques cannot be applied in this setting, we derive new tools to define such models in our framework. We empirically demonstrate the applicability of our methods to a number of synthetic and real-world tasks, including the constrained conformational modelling of protein backbones and robotic arms

Drug Discovery under Covariate Shift with Domain-Informed Prior Distributions over Functions

Accelerating the discovery of novel and more effective therapeutics is an important pharmaceutical problem in which deep learning is playing an increasingly significant role. However, real-world drug discovery tasks are often characterized by a scarcity of labeled data and significant covariate shift\unicode{x2013}\unicode{x2013}a setting that poses a challenge to standard deep learning methods. In this paper, we present Q-SAVI, a probabilistic model able to address these challenges by encoding explicit prior knowledge of the data-generating process into a prior distribution over functions, presenting researchers with a transparent and probabilistically principled way to encode data-driven modeling preferences. Building on a novel, gold-standard bioactivity dataset that facilitates a meaningful comparison of models in an extrapolative regime, we explore different approaches to induce data shift and construct a challenging evaluation setup. We then demonstrate that using Q-SAVI to integrate contextualized prior knowledge of drug-like chemical space into the modeling process affords substantial gains in predictive accuracy and calibration, outperforming a broad range of state-of-the-art self-supervised pre-training and domain adaptation techniques.Comment: Published in the Proceedings of the 40th International Conference on Machine Learning (ICML 2023

Metropolis Sampling for Constrained Diffusion Models

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling. Their extension to Riemannian manifolds has facilitated their application to an array of problems in the natural sciences. Yet, in many practical settings, such manifolds are defined by a set of constraints and are not covered by the existing (Riemannian) diffusion model methodology. Recent work has attempted to address this issue by employing novel noising processes based on logarithmic barrier methods or reflected Brownian motions. However, the associated samplers are computationally burdensome as the complexity of the constraints increases. In this paper, we introduce an alternative simple noising scheme based on Metropolis sampling that affords substantial gains in computational efficiency and empirical performance compared to the earlier samplers. Of independent interest, we prove that this new process corresponds to a valid discretisation of the reflected Brownian motion. We demonstrate the scalability and flexibility of our approach on a range of problem settings with convex and non-convex constraints, including applications from geospatial modelling, robotics and protein design