Exact simulation of diffusions and improved algorithms for log-concave sampling

What the math gives to ML

The paper provides a constructive way to turn a diffusion with a known target density into an exact path-space rejection sampler, using Girsanov density ratios and unbiased estimators that require only a constant number of potential-gradient queries when the time horizon is chosen appropriately. The transferable asset is not merely underdamped Langevin dynamics, but the possibility of correcting an approximate stochastic trajectory without discretization bias by accepting or rejecting an entire path. This suggests an inference-time sampler for energy-based or score-based neural models: use a cheap approximate underdamped proposal, then apply an unbiased likelihood-ratio correction and measure success against MALA or ordinary discretized Langevin at equal gradient-query budgets.