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			<titleStmt><title level='a'>Normalization-equivariant Diffusion Models: Learning Posterior Samplers From Noisy And Partial Measurements,</title></titleStmt>
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				<publisher>International Conference on Machine Learning</publisher>
				<date>07/06/2026</date>
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				<bibl> 
					<idno type="par_id">10696767</idno>
					<idno type="doi"></idno>
					
					<author>Brett Levac</author><author>Jonathan Tamir</author><author>Marcelo Pereyra</author><author>Julian Tachella</author>
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			<abstract><ab><![CDATA[Diffusion models (DMs) are a powerful frame-work for image generation and restoration. How-ever, existing DMs are primarily trained in a su-pervised manner by using a large corpus of cleanimages. This poses fundamental challenges inmany real-world scenarios, where acquiring noise-free data is hard or infeasible. While some meth-ods are capable of training DMs using noisy data,they are effective only when the amount of noiseis very mild or when additional noise-free datais available. In addition, existing methods fortraining DMs from incomplete measurements re-quire access to multiple complementary acquisi-tion processes, a significant practical limitation.Here we introduce the first approach for learningDMs for image restoration using only noisy mea-surement data from a single operator. First, weshow that DMs, and more broadly minimum meansquared error denoisers, exhibit a weak form ofscale equivariance linking rescaling in signal am-plitude to changes in noise intensity. We thenleverage this theoretical insight to develop a de-noising score-matching strategy that generalizesrobustly to noise levels below the training data,thereby enabling the learning of DMs from noisymeasurements. For problems involving measure-ments both noisy and incomplete, we integrate ourmethod with equivariant imaging, a complemen-tary self-supervised learning framework that ex-ploits the inherent invariants of imaging problems.This allows training DMs for image restorationfrom single-operator noisy measurements. Wevalidate the effectiveness of our approach throughextensive experiments on image denoising, demo-saicing, inpainting, and MRI reconstruction along with comparisons with the state of the art.]]></ab></abstract>
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