Sampling in discrete spaces, with critical applications in simulation and optimization, has recently been boosted by significant advances in gradient-based approaches that exploit modern accelerators like GPUs. However, two key challenges are hindering further advancement in research on discrete sampling.

Sampling from probability distributions is a crucial task in both statistics and machine learning. However, when the target distribution does not permit exact sampling, researchers often rely on Markov chain Monte Carlo (MCMC) methods.

Sampling from a high-dimensional distribution serves as one of the key components in statistics, machine learning, and scientific computing, and constitutes the foundation of the fields including Bayesian statistics and generative models [Liu and Liu, 2001, Brooks et al., 2011, Song et al.,

Sampling from a high-dimensional distribution serves as one of the key components in statistics, machine learning, and scientific computing, and constitutes the foundation of the fields including Bayesian statistics and generative models [Liu and Liu, 2001, Brooks et al., 2011, Song et al.,

Different distribution shifts require different algorithmic and operational interventions. Methodological research must be grounded by the specific shifts they address.

The performance of deep learning models heavily relies on the quality of the training data.

In fact, in a particular limit, the optimal path is arithmetic.