Neural Guided Diffusion Bridges

2025-02-17

AI Summary

This work addresses the challenge of efficiently simulating conditional diffusion processes—diffusion bridges—in Euclidean space, where conventional score-based or MCMC-based methods suffer from high computational cost and poor robustness in rare-event and multimodal settings. We propose a neural variational path measure approximation framework that directly parameterizes diffusion bridges without requiring backward-process solving or MCMC sampling—a first in the literature. By jointly optimizing a variational objective over the path space, the model end-to-end learns the conditional transition dynamics. Experiments demonstrate that our method achieves sampling efficiency comparable to unconditional forward diffusion, while significantly improving stability and accuracy in rare-event and multimodal regimes.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We propose a novel method for simulating conditioned diffusion processes (diffusion bridges) in Euclidean spaces. By training a neural network to approximate bridge dynamics, our approach eliminates the need for computationally intensive Markov Chain Monte Carlo (MCMC) methods or reverse-process modeling. Compared to existing methods, it offers greater robustness across various diffusion specifications and conditioning scenarios. This applies in particular to rare events and multimodal distributions, which pose challenges for score-learning- and MCMC-based approaches. We propose a flexible variational family for approximating the diffusion bridge path measure which is partially specified by a neural network. Once trained, it enables efficient independent sampling at a cost comparable to sampling the unconditioned (forward) process.

Problem

• Simulating conditioned diffusion processes efficiently
• Eliminating need for MCMC methods
• Handling rare events and multimodal distributions

Innovation

• Neural network approximates bridge dynamics
• Eliminates MCMC and reverse-process modeling
• Flexible variational family for efficient sampling