Control Consistency Losses for Diffusion Bridges

arXiv stat.ML / 4/23/2026

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Key Points

The paper addresses the problem of simulating diffusion processes conditioned on both initial and terminal states, which is especially difficult for rare events where standard dynamics seldom reach the target.
It introduces a learning method for diffusion bridges that leverages a self-consistency property of optimal control.
The proposed algorithm learns the conditioned dynamics iteratively in an online manner, improving practicality for training and updating.
The method demonstrates strong empirical performance across multiple settings while avoiding differentiation through simulated trajectories.
The authors also relate their self-consistency framework to recent developments in stochastic optimal control, extending the work’s relevance beyond diffusion bridges.

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 propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.