发表机构
College of Computer Science, Sichuan University（四川大学计算机学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对潜在流模型应用于逆问题的一阶流形盲区瓶颈，提出混合域后验采样框架，结合朗之万动力学与潜在对齐，在多类逆问题上取得新的最优性能。
AI 中文摘要
潜在流模型已彻底改变压缩空间图像合成，但应用于高保真逆问题仍存在瓶颈。本文将该困境归因于预训练自编码器的基本几何局限，我们称之为“一阶流形盲区”。严重的解码器压缩（例如仅保留约2%的原始自由度）会产生秩亏雅可比矩阵，即使解码器能表示目标图像，其正交补空间中的高频测量残差对潜在梯度也不可见。为克服该瓶颈，我们提出混合域后验采样（HDPS），这是一种解耦推理框架，将物理测量一致性与语义先验建模分离。HDPS在像素空间中发散，利用朗之万动力学吸收精确的正交测量梯度，随后将这些结构校正投影回生成流形。引入基于优化的潜在对齐以过滤像素空间伪影，同时避免直接编码的语义漂移。对多种逆问题的大量实验表明，HDPS达到了新的 state-of-the-art，成功恢复了仅潜在求解器固有丢弃的高频结构精度。代码可在 this https URL 获取。
英文摘要
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}.
CommentsAccepted to ACM Multimedia 2026
