Diffusion models learn a velocity field that matches the Wasserstein gradient flow of the OU process, not a true score, and errors in the Stein null space leave density transport exact.
Diffusion Models and Gaussian Flow Matching: Two Sides of the Same Coin
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Are We Really Learning the Score Function? Reinterpreting Diffusion Models Through Wasserstein Gradient Flow Matching
Diffusion models learn a velocity field that matches the Wasserstein gradient flow of the OU process, not a true score, and errors in the Stein null space leave density transport exact.