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Newton Matching for Generative Modeling: A Unified Framework for Fine-Tuning and Sampling

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

We develop Newton Matching, a unified framework for fine-tuning and sampling in generative modeling. The target is $π\proptoμe^{τr}$, where $r$ is the reward, $τ>0$ the inverse temperature, and $μ$ denotes the pretrained model's terminal density for fine-tuning or the constant $1$ for sampling. We shift the paradigm from isolated losses to iterative optimization over canonical models: population minimizers of standard conditional matching for terminal densities. Under compatible smooth-realization assumptions, canonical velocities form a manifold diffeomorphic to the density manifold. Transpor

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