[2601.23280] Decoupled Diffusion Sampling for Inverse Problems on Function Spaces

Computer Science > Machine Learning arXiv:2601.23280 (cs) [Submitted on 30 Jan 2026 (v1), last revised 2 Mar 2026 (this version, v3)] Title:Decoupled Diffusion Sampling for Inverse Problems on Function Spaces Authors:Thomas Y.L. Lin, Jiachen Yao, Lufang Chiang, Julius Berner, Anima Anandkumar View a PDF of the paper titled Decoupled Diffusion Sampling for Inverse Problems on Function Spaces, by Thomas Y.L. Lin and 4 other authors View PDF Abstract:We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling, requiring substantial paired supervision. In contrast, our Decoupled Diffusion Inverse Solver (DDIS) employs a decoupled design: an unconditional diffusion learns the coefficient prior, while a neural operator explicitly models the forward PDE for guidance. This decoupling enables superior data efficiency and effective physics-informed learning, while naturally supporting Decoupled Annealing Posterior Sampling (DAPS) to avoid over-smoothing in Diffusion Posterior Sampling (DPS). Theoretically, we prove that DDIS avoids the guidance attenuation failure of joint models when training data is scarce. Empirically, DDIS achieves state-of-the-art performance under sparse observation, improving $l_2$ error by 11% and spectral error by 54% on average; when data is limited to 1%, DDIS maintains accuracy with 4...