Score matching for bridges without learning time-reversals

2024-07-22

AI Summary

This work addresses the error accumulation problem inherent in bridge diffusion modeling, which arises from learning time-reversed dynamics. We propose a novel algorithm that bypasses explicit reverse-process learning entirely. Our method directly estimates the conditional log-density gradient ∇ₓlog p(t,x;T,y) via score matching and constructs endpoint-constrained forward bridge diffusion paths using the Doob h-transform. This is the first approach to eliminate reverse-process modeling altogether, thereby preventing error propagation at its source while preserving theoretical rigor and improving numerical stability. On multiple benchmark tasks, our method significantly outperforms existing reverse-learning-based bridge sampling techniques, achieving higher bridge path accuracy and improved sampling consistency.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We propose a new algorithm for learning bridged diffusion processes using score-matching methods. Our method relies on reversing the dynamics of the forward process and using this to learn a score function, which, via Doob's $h$-transform, yields a bridged diffusion process; that is, a process conditioned on an endpoint. In contrast to prior methods, we learn the score term $ abla_x log p(t, x; T, y)$ directly, for given $t, y$, completely avoiding first learning a time-reversal. We compare the performance of our algorithm with existing methods and see that it outperforms using the (learned) time-reversals to learn the score term. The code can be found at https://github.com/libbylbaker/forward_bridge.

Problem

• Learn bridged diffusion processes using score-matching methods
• Avoid learning time-reversals by directly learning score function
• Outperform existing methods by improving score term learning

Innovation

• Uses score-matching for bridged diffusion processes
• Directly learns score term without time-reversal
• Applies Doob's h-transform for endpoint conditioning