Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs

• URL: http://arxiv.org/abs/2410.11149v1
• Date: Tue, 15 Oct 2024 00:23:09 GMT
• Title: Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costs
• Authors: Severi Rissanen, Markus Heinonen, Arno Solin,
• Abstract summary: Covariance information is available for free from training data and the curvature of the generative trajectory. We integrate these sources of information using em (i) a novel method to transfer covariance estimates across noise levels. We validate the method on linear inverse problems, where it outperforms recent baselines.
• Score: 25.784316302130875
• License:
• Abstract: The covariance for clean data given a noisy observation is an important quantity in many conditional generation methods for diffusion models. Current methods require heavy test-time computation, altering the standard diffusion training process or denoiser architecture, or making heavy approximations. We propose a new framework that sidesteps these issues by using covariance information that is available for free from training data and the curvature of the generative trajectory, which is linked to the covariance through the second-order Tweedie's formula. We integrate these sources of information using {\em (i)} a novel method to transfer covariance estimates across noise levels and (ii) low-rank updates in a given noise level. We validate the method on linear inverse problems, where it outperforms recent baselines, especially with fewer diffusion steps.

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