Hybrid-Domain Posterior Sampling for Inverse Problems via Latent Flow Matching

2026-08-01

AI Summary

This work addresses the limitations of pretrained autoencoders in high-fidelity inverse problem solving, where first-order manifold blind spots hinder the perception of high-frequency measurement residuals, thereby constraining reconstruction quality. To overcome this, the authors propose a Hybrid-Domain Posterior Sampling (HDPS) framework that decouples physical consistency from semantic priors: it incorporates orthogonal measurement gradients in the pixel domain via Langevin dynamics, projects structural corrections back onto the generative manifold, and simultaneously optimizes the latent representation to align semantics and suppress artifacts. This approach is the first to explicitly identify and mitigate the first-order manifold blind spot of autoencoders under severe compression, enabling accurate recovery of high-frequency structures. Extensive experiments demonstrate state-of-the-art performance across multiple inverse problems, significantly improving both reconstruction fidelity and fine-detail accuracy.

Abstract

Latent Flow Models have revolutionized compressed-space image synthesis, yet their application to high-fidelity inverse problems remains bottlenecked. In this paper, we trace this dilemma to a fundamental geometric limitation of pre-trained autoencoders, which we term \emph{First-Order Manifold Blindness}. Severe decoder compression (e.g., retaining only $\sim\!2\%$ of the original degrees of freedom) produces a rank-deficient Jacobian, rendering high-frequency measurement residuals in its orthogonal complement invisible to latent gradients even when the decoder can represent the target image. To overcome this bottleneck, we propose Hybrid-Domain Posterior Sampling (HDPS), a decoupled inference framework that disentangles physical measurement consistency from semantic prior modeling. HDPS diverges into the pixel space, leveraging Langevin dynamics to absorb precise orthogonal measurement gradients, and subsequently projects these structural corrections back onto the generative manifold. An optimization-based latent alignment is introduced to filter pixel-space artifacts while avoiding the semantic drift of direct encoding. Extensive experiments on diverse inverse problems demonstrate that HDPS establishes a new state-of-the-art, successfully recovering the high-frequency structural precision that latent-only solvers inherently discard. The code is available at \href{https://github.com/74587887/HDPS}{https://github.com/74587887/HDPS}.

Problem

• inverse problems
• latent space
• high-frequency recovery
• manifold blindness
• autoencoder

Innovation

• Latent Flow Matching
• Inverse Problems
• Manifold Blindness
• Hybrid-Domain Sampling
• Langevin Dynamics