Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we obtain Wasserstein discretization bounds for Euler-type samplers in dimension $d$: with $N$ discretization steps, the error achieves the optimal rate $\sqrt{d}/N$ up to logarithmic factors. Moreover, the constants do not deteriorate exponentially with the spatial extent of $p^\star$. We also show that the one-sided Lipschitz control yields a globally Lipschitz transport map from the standard Gaussian to $p^\star$, which implies Poincaré and log-Sobolev inequalities for a broad class of probability measures.

Our estimators assume that there is no interference between the units, i.e., that the treatment of one The first assumption is quite realistic as in most peer review systems the reviewers cannot see other reviews until they submit their own. The second assumption is important to understand, as there could be "batch effects": a Monte Carlo methods to tightly estimate these covariances. AAAI datasets, we sampled 1 million assignments and computed the empirical covariance. In our setting, small amounts of attrition (relative to the number of policy-induced positivity violations) mean that the fraction of data that is missing is not exactly known before assignment, but almost. To get more robust estimates of the performance, we repeat this process 10 times.

We consider the problem of extracting a reward function by comparing a decision-making diffusion model that models low-reward behavior and one that models high-reward behavior; a setting related to inverse reinforcement learning. We first define the notion of a relative reward function of two diffusion models and show conditions under which it exists and is unique.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/