Score Accuracy Under Forward Diffusion Does Not Certify Reverse-Sampler Stability

arXiv·medium signal

Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory, not the forward one. This paper (arXiv 2607.08757, July 9) constructs a smooth score field with arbitrarily small forward-marginal L2 error whose reverse-time process is nonexplosive, has moments of every order, and is arbitrarily close to the exact process in path-space total variation — yet the discretized sampler is still numerically unstable. The practical takeaway is that a good score-matching loss is not a stability guarantee for the sampler you actually ship.