MACS: Measurement-Aware Consistency Sampling for Inverse Problems

TL;DR

The paper tackles the computational bottleneck of inverse-problem solving with diffusion priors by adapting Consistency Models through a measurement-aware sampling scheme. MACS replaces the variance-based stochasticity in aDDIM with a residual-based term that enforces data fidelity via the forward operator, enabling fast, few-step reconstructions. Empirical results on Fashion-MNIST and LSUN Bedroom demonstrate consistent improvements in perceptual metrics (FID, KID) and retention of competitive pixel-level metrics (PSNR, SSIM) with only two sampling steps. The approach is plug-and-play, requiring no retraining of the CM backbone, and shows strong potential for practical deployment of CM-based inverse solvers.

Abstract

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.

Figures (4)

• Figure 1: Illustration of the proposed MACS framework. The diagram shows the iterative sampling process in which measurement consistency is enforced through the residual term. The CM $f_\theta$ denoises the noisy latent $\boldsymbol{x}_t$ conditioned on the measurements $\boldsymbol{y}$, and the MACS update adaptively adjusts the stochasticity based on this residual.
• Figure 2: Visual comparison across four inverse problems on the LSUN Bedroom dataset: inpainting (top row), linear deblurring (second row), super-resolution (third row), and nonlinear deblurring (bottom row). Each row shows the ground truth, measurement, our MACS reconstruction, and outputs from four fast-sampling baselines (DPM-Solver, Heun, Euler, and Multistep). MACS consistently reconstructs sharper edges and more details compared to other fast samplers.
• Figure 3: Visual comparison on three inverse problems from the Fashion-MNIST dataset: inpainting (top), linear deblurring (middle), and super-resolution (bottom). Each row shows the ground truth, the measurement, our MACS reconstruction, and the outputs of four fast-sampling baselines. MACS yields clearer structures and more details than the other methods.
• Figure 4: Normalized measurement residue as a function of NFEs for MACS on the (a) LSUN Bedroom and (b) Fashion-MNIST datasets. MACS achieves most of its reduction in measurement residue within the first two steps across all inverse problems, after which the residue plateaus.