在扩散与流匹配后验采样中正确设置引导权重
Getting Your Guidance Weights Right in diffusion and flow-matching posterior sampling
- Heriot-Watt University, EPS（赫瑞-瓦特大学，工程与物理科学学院）
- IMS (Univ. Bordeaux, CNRS, BINP)（IMS（波尔多大学，法国国家科学研究中心，BINP））
- ONERA（法国国家航空航天研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种离线自动调优扩散与流匹配后验采样中引导权重的方法，将其化为二维线性最小二乘问题，无需重训，提升重建性能并可将采样步数降至50步。
AI中文摘要：
免训练的后验采样方法，也称为即插即用方法，利用预训练的无条件扩散或流匹配模型来解决逆问题。现有的大多数方法依赖引导权重来在每个时间步平衡来自无条件得分或速度网络的先验信息与测量一致性，然而这些权重的调整往往未被讨论，且在很大程度上留给启发式方法。我们提出了一种简单且有原则的离线策略，用于自动调整这些引导权重。我们的关键观察是，在每个时间步，扩散模型的条件去噪得分匹配目标，或流匹配模型的条件流匹配目标，是一个最小二乘目标。因此，当条件预测被表示为无条件网络输出与测量引导项的加权和时，对这些权重的优化简化为一个二维线性最小二乘问题。由此得到的与时间相关的引导权重可以在给定测量算子、噪声水平和采样器的情况下，以单批采样轨迹为代价离线优化，无需重新训练或微调预训练生成模型。以标准的基于Tweedie的测量一致性项实例化后，我们的方法改进了后验采样，并在基于扩散和流匹配的方法中实现了最先进的重建性能。此外，优化的引导权重使扩散采样器能够将采样步数从1000减少到50，而重建质量无明显下降。代码将公开提供。
英文摘要：
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.
