New paper explains why diffusion models don't need noise conditioning via Riemannian geometry
prof_kamilov · x · 2026-10-30
Google researchers Mojtaba Sahraee-Ardakan, Mauricio Delbracio and Peyman Milanfar presented "The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning" (arXiv:2602.18428) at the Asilomar Conference.
- The paper studies autonomous (noise-agnostic) generative models like Equilibrium Matching and blind diffusion, which learn a single time-invariant vector field without explicit noise conditioning.
- It formalizes "Marginal Energy" Emarg(u) = -log p(u) and proves generation in these models is a Riemannian gradient flow on that landscape, not merely blind denoising.
- Key result: although the raw energy landscape has a 1/t^p singularity normal to the data manifold, the learned field implicitly encodes a local conformal metric that exactly counteracts the singularity — resolving why noise-agnostic networks remain stable near the data manifold.
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