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conditional score estimator

A conditional score estimator is a computational method or model designed to estimate the gradient of the log-conditional probability density function with respect to a data variable given a specific condition or observation. Within score-based generative modeling and diffusion frameworks, it calculates the conditional score function, which directs the generative trajectory by combining the prior score of the data distribution with a guidance gradient derived from the conditioning information. By steering the reverse-time diffusion process along this conditional vector field, the estimator enables the generation of high-fidelity samples that conform to external measurements, class labels, or inverse-problem constraints without necessarily requiring a fully supervised model for every specific downstream task.

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Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior

Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior

Tongda Xu, Xiyan Cai, Xinjie Zhang, Xingtong Ge, Dailan He, Liming Sun, Jingjing Liu, Ya-Qin Zhang, Jian Li, Yan Wang

OrganizationsKuaishou TechnologyNew York UniversitySenseTimeThe Chinese University of Hong KongThe Hong Kong University of Science and TechnologyTsinghua UniversityUniversity of Cambridge

Why you should read this

Demonstrates that Diffusion Posterior Sampling functions as maximum a posteriori optimization rather than true conditional score matching, introducing explicit posterior maximization and an ultra-lightweight estimator trained on just 100 images to improve diffusion-based inverse problem solving.

Recent advancements in diffusion models have been leveraged to address inverse problems without additional training, and Diffusion Posterior Sampling (DPS) (Chung et al., 2022a) is among the most popular approaches. Previous analyses suggest that DPS accomplishes posterior sampling by approximating the conditional score. While in this paper, we demonstrate that the conditional score approximation employed by DPS is not as effective as previously assumed, but rather aligns more closely with the principle of maximizing a posterior (MAP). This assertion is substantiated through an examination of DPS on 512x512 ImageNet images, revealing that: 1) DPS's conditional score estimation significantly diverges from the score of a well-trained conditional diffusion model and is even inferior to the unconditional score; 2) The mean of DPS's conditional score estimation deviates significantly from zero, rendering it an invalid score estimation; 3) DPS generates high-quality samples with significantly lower diversity. In light of the above findings, we posit that DPS more closely resembles MAP than a conditional score estimator, and accordingly propose the following enhancements to DPS: 1) we explicitly maximize the posterior through multi-step gradient ascent and projection; 2) we utilize a light-weighted conditional score estimator trained with only 100 images and 8 GPU hours. Extensive experimental results indicate that these proposed improvements significantly enhance DPS's performance. The source code for these improvements is provided in this https URL.

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2026-10-01