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

arXiv: https://arxiv.org/abs/2610.03503 · HTML: https://mlsanity.com/paper/2610.03503/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 39 of its 49 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 39)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Elucidating the Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2308.15321/) (2023)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [FlowDPS: Flow-Driven Posterior Sampling for Inverse Problems](https://mlsanity.com/paper/2503.08136/) (2025)

## Abstract (arXiv)

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.