Control Consistency Losses for Diffusion Bridges

2025-12-04

AI Summary

This work addresses the problem of simulating conditional diffusion paths between prescribed initial and final states under rare-event regimes—where standard unconditional diffusion rarely reaches the target state. To overcome this, we propose an online iterative learning framework grounded in consistency loss, leveraging the self-consistency of conditional diffusion dynamics to define the objective without explicit density estimation or prior path assumptions. Our method integrates diffusion modeling with optimal control principles, iteratively optimizing an implicit representation of the diffusion bridge. Experiments demonstrate substantial improvements in path generation stability and accuracy across diverse settings, particularly outperforming existing diffusion-bridge techniques for low-probability events. The approach establishes a scalable, model-free paradigm for conditional path sampling, eliminating the need for hand-crafted stochastic differential equations or likelihood-based inference.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we leverage a self-consistency property of the conditioned dynamics to learn the diffusion bridge in an iterative online manner, and demonstrate promising empirical results in a range of settings.

Problem

• Simulating conditioned diffusion dynamics between states
• Addressing rare events with low unconditional transition probability
• Learning diffusion bridges via iterative self-consistency methods

Innovation

• Self-consistency property for conditioned dynamics
• Iterative online learning of diffusion bridge
• Simulating rare events with initial-terminal states