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Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression

arXiv · AI, language, vision and robotics · article · Sep 4, 2026 · UTC

We study variance-preserving diffusion of the response in mixed linear regression (MLR) with unknown mixing weights. Our analysis separates the statistical guarantees of score matching from the loss geometry and optimization signal at a fixed diffusion noise level. The KL divergence links the denoising score matching objective integrated over the diffusion path with the likelihood and a terminal discrepancy. Under mild regularity conditions and terminal schedule, the resulting estimator converges up to the ground truth parameters of MLR, and its scaled error converges to the Gaussian limit of

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