A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling

2026-06-10 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Optimization & Control · Depth: Expert, quick

Summary

A new stabilized path-space framework has been developed for diffusion-based posterior sampling, addressing limitations of current heuristic guidance approximations that often fail for nonlinear operators and multimodal posteriors in Bayesian inverse problems. This approach defines a likelihood-weighted target measure on trajectories, framing posterior sampling as learning a controlled stochastic process to match this target. It integrates diffusion posterior sampling with stochastic optimal control while maintaining Bayesian uncertainty quantification. A crucial innovation is a time reparameterization technique that resolves bias from unknown initial value functions, making the path-space control problem well-posed without requiring auxiliary training. The control is then learned through a trust-region path-space optimization method utilizing log-variance objectives. This framework also unifies learned control with existing guidance-based samplers, quantifies sampling error, and provides importance sampling corrections for exact posterior expectations. Evaluations on benchmark inverse problems demonstrate enhanced accuracy and robustness compared to leading methods.

Key takeaway

For research scientists working on Bayesian inverse problems, if you are struggling with the limitations of heuristic guidance in diffusion posterior samplers, consider this stabilized path-space framework. It offers improved accuracy and robustness, especially for nonlinear operators and multimodal posteriors, by integrating stochastic optimal control and a novel bias-removing time reparameterization. You should investigate its application to your specific inverse problems to enhance uncertainty quantification.

Key insights

A stabilized path-space framework improves diffusion posterior sampling by connecting it to stochastic optimal control and removing bias.

Principles

• Likelihood-weighted target measures define posterior sampling.
• Time reparameterization can remove control problem bias.
• Path-space optimization quantifies sampling error.

Method

Define a likelihood-weighted target measure on trajectories. Learn a controlled stochastic process via trust-region path-space optimization, using time reparameterization to remove initial value function bias.

In practice

• Apply to Bayesian inverse problems.
• Assess sampling accuracy and uncertainty.
• Improve robustness over existing methods.

Topics

• Diffusion Models
• Posterior Sampling
• Bayesian Inverse Problems
• Stochastic Optimal Control
• Uncertainty Quantification
• Path-Space Optimization

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.