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

Liam Moroy; Jean-François Giovannelli; Yoann Altmann; Steve McLaughlin; Frédéric Champagnat; Guillaume Bourmaud

cs.LGOct 2, 2026

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

Authors: Liam Moroy, Jean-François Giovannelli, Yoann Altmann, Steve McLaughlin, Frédéric Champagnat, Guillaume Bourmaud

Organizations: Heriot-Watt University, EPS Edinburgh, UK · IMS (Univ. Bordeaux, CNRS, BINP) Bordeaux, France · ONERA Paris, France

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.

Figures & tables

Panel of Figure 1 — Figure 1: Guidance weights from SIMCA: $w_{u,t}$ (left) and $w_{f,t}$ (right, log scale) on FFHQ at $K=1000$ , for box inpainting , random inpainting and super-resolution .

Panel of Figure 2 — Figure 2: Qualitative comparison on the box inpainting task. SIMCA produces completions coherent with the visible context, whereas the baselines oversmooth the fill, hallucinate details, leak colours, or produce dark or discoloured fills.

Task	Method	FFHQ				ImageNet
Task	Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
SR $\times 4$	DAPS	29.07	0.818	0.177	51.44	25.89	0.694	0.276	83.57
	DPS	25.86	0.753	0.269	81.07	21.13	0.489	0.361	106.32
	DDRM	26.58	0.782	0.282	79.25	22.62	0.521	0.324	103.85
	DDNM	28.03	0.795	0.197	64.62	23.96	0.604	0.475	98.62
	FPS-SMC	28.42	0.813	0.204	49.25	24.82	0.703	0.313	97.51

Table 1: Reconstruction quality on FFHQ and ImageNet. Within each task, best values are in Bold and second best are underlined . SIMCA-

K

denotes calibration and sampling with

K

steps.

	Denoising			Deblurring			Super-resolution			Random inpainting			Box inpainting
Method	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS
PnP-GS	32.64	0.910	0.035	34.03	0.924	0.041	31.31	0.892	0.064	29.22	0.875	0.070	–	–	–
DiffPIR	31.20	0.885	0.060	32.77	0.912	0.060	31.52	0.895	0.033	31.74	0.917	0.025	–	–	–
OT-ODE	30.54	0.859	0.032	33.01	0.921	0.029	31.46	0.907	0.025	28.68	0.871	0.051	29.40	0.920	0.038
D-Flow	26.04	0.607	0.092	31.25	0.854	0.038	30.47	0.843	0.026	33.67	0.943	0.015	30.70	0.899	0.026
Flow-Priors	29.34	0.768	0.134	31.54	0.858	0.056	28.35	0.713	0.102	32.88	0.871	0.019	30.07	0.858	0.048

Table 2: Results on 100 test images of the dataset CelebA.

	Denoising			Deblurring			Super-resolution			Random inpainting			Box inpainting
Method	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS	PSNR	SSIM	LPIPS
PnP-GS	32.58	0.894	0.072	27.91	0.753	0.349	24.15	0.632	0.362	29.42	0.836	0.126	–	–	–
DiffPIR	30.58	0.835	0.189	27.56	0.728	0.342	23.65	0.624	0.402	31.70	0.881	0.062	–	–	–
OT-ODE	30.03	0.815	0.076	27.06	0.713	0.123	25.91	0.716	0.108	29.40	0.839	0.090	24.62	0.875	0.085
D-Flow	26.13	0.574	0.175	27.82	0.721	0.164	24.64	0.601	0.190	32.20	0.894	0.040	26.26	0.842	0.077
Flow-Priors	29.41	0.763	0.153	26.47	0.700	0.181	23.51	0.570	0.272	32.37	0.906	0.047	26.20	0.818	0.118

Table 3: Results on 100 test images of the dataset AFHQ-Cat.

Table 6

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 4 — Figure 4: SIMCA calibrated prior weights $w_{u,t}$ (left column) and likelihood weights $w_{f,t}$ (right column, log scale) over diffusion step $t$ , for AFHQ-CAT (top row) and CelebA (bottom row). Colors indicate task: Box inpainting , Random inpainting , Super resolution , Denoising , and Gaussian blur .

Figure 5: SIMCA on FFHQ box inpainting at $K=1000$ , $500$ and $50$ steps, recalibrated at each discretization.

Figure 6: SIMCA on FFHQ random inpainting at $K=1000$ , $500$ and $50$ steps, recalibrated at each discretization.

Figure 7: SIMCA on FFHQ Gaussian deblurring at $K=1000$ , $500$ and $50$ steps, recalibrated at each discretization.

Figure 8: SIMCA on FFHQ motion deblurring at $K=1000$ , $500$ and $50$ steps, recalibrated at each discretization.

Figure 9: SIMCA on FFHQ super-resolution at $K=1000$ , $500$ and $50$ steps, recalibrated at each discretization.

		Random Inpainting				Box Inpainting				SRx4
Samplers	K	PSNR	SSIM	LPIPS	FID	PSNR	SSIM	LPIPS	FID	PSNR	SSIM	LPIPS	FID
DDPM	1000	32.91	0.916	0.069	19.16	22.90	0.846	0.106	43.68	29.12	0.821	0.145	46.39
	500	33.07	0.920	0.068	18.31	23.28	0.850	0.105	39.77	29.26	0.826	0.143	43.14
	200	33.34	0.926	0.068	20.76	23.28	0.853	0.106	43.26	29.48	0.836	0.141	44.51
	100	33.62	0.930	0.068	23.04	23.36	0.856	0.108	44.52	29.71	0.845	0.140	45.50
	50	33.76	0.930	0.072	24.88	23.43	0.855	0.110	47.12	30.00	0.853	0.144	49.02

Appendix

Table 6: Effect of the sampler and the discretization, on FFHQ. SIMCA is recalibrated independently for each sampler and step count

K

. Stochastic samplers (DDPM, Euler-Maruyama) outperform their deterministic counterparts (DDIM, Euler-ODE) at every budget, and DDPM alone remains stable down to

K=50

where it attains the best distortion metrics of the table on random inpainting and super-resolution.

Diffusion Posterior Sampling

Diffusion posterior sampling combines generative diffusion priors with measurement models to infer plausible solutions and uncertainty in inverse problems.

See all 81 papers

Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning
Oct 9, 2026Teo Deveney, Lea Bogensperger, Hok Shing WongPosterior Sampling Diffusion Posterior Sampling
University of Bath · University of Zurich · LMU Munich
What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View
Jun 23, 2026Jian Xu, Delu Zeng, John Paisley +1Flow Matching Bayesian Inverse Problems
1RIKEN iTHEMS · 2RIKEN AIP · 3South China University of Technology +1
Prediction--Loss Alignment for Sampler--Robust Flow Matching Training
Feb 11, 2026Jiadong Hong, Lei Liu, Xinyu Bian +2Flow Matching Diffusion Sampling
Zhejiang University, Hangzhou, China · Huawei Technologies Co., Ltd, Hong Kong

Oct 9, 2026J/K move · Enter open · S save

Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning

Teo Deveney, Lea Bogensperger, Hok Shing Wong

University of Bath · University of Zurich · LMU Munich

Posterior Sampling Diffusion Posterior Sampling Flow-Based Generative Modeling Bayesian Inverse Problems

Open paper AskPDF arXiv

Flow-matching and diffusion models are increasingly used as priors for linear inverse problems, however, most methods are bespoke to one class of trajectory prior. Plug-and-play methods have been proposed, however these implicitly decorrelate the guided trajectory, resulting in broad priors that can struggle when data is sparse. This work proposes

β

-Flow: a general plug-and-play method indexed by a correlation parameter

β

that generalises over flow, diffusion, and decorrelated priors, and a confidence parameter

κ

that controls how strongly the path distribution is enforced. Each step requires only one forward evaluation of a denoising network, followed by a Gaussian conditioning step. This step is an exact Kalman update that is not dependent on network gradients. We show that many existing guided samplers can be interpreted as instances or approximations of our method, each implicitly using a different trajectory prior and operator in place of the Kalman gain. From this viewpoint, we provide a qualitative comparison of methods in terms of their implicit biases and assumptions. We demonstrate consistently state-of-the-art level performance across 7 inverse problems over 4 datasets in terms of PSNR and SSIM. Moreover, we demonstrate the utility of this prior control, by showing that confident high correlations (strict priors) work best when observations are less informative, while low correlation is preferred when observations are more informative, reflecting the complementary roles of the prior and likelihood in Bayesian inference.

Abstract

Diffusion Posterior Sampling

Explore similar work

Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning

What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View

Prediction--Loss Alignment for Sampler--Robust Flow Matching Training