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This paper addresses the heuristic tuning of guidance weights in training-free posterior sampling for diffusion and flow-matching models by reformulating the conditional denoising/flow-matching objective as a least-squares problem. By optimizing a weighted sum of the unconditional network output and a measurement-guidance term, time-dependent guidance weights are derived via a 2D linear least-squares solution. This offline optimization, requiring only a single minibatch of trajectories, yields state-of-the-art reconstruction performance and enables significant reductions in sampling steps without quality degradation.
Optimal guidance weights for diffusion and flow-matching posterior sampling can be found with a simple offline linear least-squares solution, drastically cutting sampling steps and boosting reconstruction quality.
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.