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[2602.18428] The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning
Summary
This paper explores the concept of noise-agnostic generative models, specifically diffusion models, and argues that they do not require explicit noise conditioning. It presents a formalization of Marginal Energy and its implications for model stability and performance.
Why It Matters
Understanding the mechanics of noise-agnostic generative models is crucial for advancing machine learning techniques. This research challenges existing paradigms, potentially leading to more robust and efficient models in fields like computer vision and artificial intelligence.
Key Takeaways
- Diffusion models can operate without explicit noise conditioning.
- Marginal Energy formalization provides insights into model stability.
- Velocity-based parameterizations enhance stability in generative models.
Computer Science > Machine Learning arXiv:2602.18428 (cs) [Submitted on 20 Feb 2026] Title:The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning Authors:Mojtaba Sahraee-Ardakan, Mauricio Delbracio, Peyman Milanfar View a PDF of the paper titled The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning, by Mojtaba Sahraee-Ardakan and 2 other authors View PDF HTML (experimental) Abstract:Autonomous (noise-agnostic) generative models, such as Equilibrium Matching and blind diffusion, challenge the standard paradigm by learning a single, time-invariant vector field that operates without explicit noise-level conditioning. While recent work suggests that high-dimensional concentration allows these models to implicitly estimate noise levels from corrupted observations, a fundamental paradox remains: what is the underlying landscape being optimized when the noise level is treated as a random variable, and how can a bounded, noise-agnostic network remain stable near the data manifold where gradients typically diverge? We resolve this paradox by formalizing Marginal Energy, $E_{\text{marg}}(\mathbf{u}) = -\log p(\mathbf{u})$, where $p(\mathbf{u}) = \int p(\mathbf{u}|t)p(t)dt$ is the marginal density of the noisy data integrated over a prior distribution of unknown noise levels. We prove that generation using autonomous models is not merely blind denoising, but a specific form of Riemannian gradient flow on this Marginal Energy. Through a novel rel...