Getting Your Guidance Weights Right in diffusion and flow-matching posterior sampling

2026-10-02

AI Summary

This study addresses the challenge of heuristically tuning guidance weights during posterior sampling in diffusion and flow matching models. We propose a training-free, offline optimization strategy that leverages the Tweedie measurement consistency term to reformulate the conditional denoising objective as a linear least-squares problem. This formulation enables the first automated weight-tuning framework capable of adaptively determining optimal per-timestep guidance weights without retraining the pre-trained generative model. Experimental results demonstrate that our framework achieves state-of-the-art reconstruction performance across diverse inverse problems while reducing the number of sampling steps from 1000 to 50 without noticeable quality degradation, thereby significantly improving both sampling efficiency and accuracy.

Abstract

Training-free posterior sampling methods, also known as Plug-and-Play methods, leverage pretrained unconditional diffusion or flow-matching models to solve inverse problems. Most existing approaches rely on guidance weights to balance, at each time step, prior information from the unconditional score or velocity network with measurement consistency, yet the tuning of these weights is often not discussed and is largely left to heuristics. We introduce a simple and principled offline strategy for automatically tuning these guidance weights. Our key observation is that, at each time step, the conditional denoising score-matching objective for diffusion models, or the conditional flow-matching objective for flow-matching models, is a least-squares objective. Therefore, when the conditional prediction is expressed as a weighted sum of the unconditional network output and a measurement-guidance term, optimizing over these weights reduces to a two-dimensional linear least-squares problem. The resulting time-dependent guidance weights can be optimized offline for a given measurement operator, noise level and sampler at the cost of a single minibatch of sampling trajectories, without retraining or fine-tuning the pretrained generative model. Instantiated with the standard Tweedie-based measurement-consistency term, our approach improves posterior sampling and achieves state-of-the-art reconstruction performance across diffusion- and flow-matching-based methods. Moreover, the optimized guidance weights enable diffusion samplers to reduce the number of sampling steps from 1000 to 50 with no significant degradation in reconstruction quality. Code will be made available.

Problem

• posterior sampling
• diffusion models
• flow-matching
• guidance weights
• inverse problems

Innovation

• Posterior Sampling
• Guidance Weights
• Diffusion Models
• Flow Matching
• Linear Least-Squares