Research Objective
We study how to learn a generative model of clean images using only noisy observations.
Requirements for Diffusion Processes
Diffusion processes and their generalizations to non-Gaussian noise require posterior predictions at every noise level.
Findings on Noise2Noise Regression
We first show that it is possible to learn these predictions from independent noisy views using Noise2Noise regression, but only at or above the noise level of the training data.
Approach: Consistency Constraint
To learn the predictions below that level, needed to generate clean images, we impose consistency: a prediction should equal its expectation after continuing the sampling process.
Theoretical Contributions
We derive conditions under which consistency uniquely determines the continuation to the clean image distribution and verify them for Poisson, binomial, Gamma, and negative-binomial measurements.
Experimental Results
Experiments on CIFAR-10, photon-counting microscopy, and synthetic aperture radar show that:
- the required posterior predictions can be learned from noisy views alone
- the consistency relation repairs the continuation beyond the noise level of the data
- performance severely deteriorates without consistency