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MAD: Manifold Attracted Diffusion
[Submitted on 29 Sep 2025 (v1), last revised 9 Jun 2026 (this ve · 2026-06-10 · via stat updates on arXiv.org

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Abstract:Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently implementable modification of the inference procedure to generate noiseless samples. Our approach is motivated by the manifold hypothesis, according to which meaningful data is concentrated around some low-dimensional manifold of a high-dimensional ambient space. The central idea is that noise manifests as low magnitude variation in off-manifold directions in contrast to the relevant variation of the desired distribution which is mostly confined to on-manifold directions. We introduce the notion of an extended score and show that, in a simplified setting, it can be used to reduce small variations to zero, while leaving large variations mostly unchanged. We describe how its approximation can be computed efficiently from an approximation to the standard score and demonstrate its efficacy on toy problems, synthetic data, and real data.

Submission history

From: Matteo Santacesaria [view email]
[v1] Mon, 29 Sep 2025 12:40:20 UTC (36,269 KB)
[v2] Tue, 9 Jun 2026 09:46:19 UTC (18,671 KB)