Sampling from Energy distributions with Target Concrete Score Identity

We introduce the Target Concrete Score Identity Sampler(TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a continuous-time Markov chain (CTMC). Our approach builds on a forward CTMC with a uniform noising kernel and relies on the proposed Target Concrete Score Identity, which relates the concrete score, the ratio of marginal probabilities of two states, to a ratio of expectations of Boltzmann factors under the forward uniform diffusion kernel . This formulation enables Monte Carlo estimation of the concrete score without requiring samples from the target distribution or computation of the partition function. We approximate the concrete score with a neural network and propose two algorithms: Self-Normalized TCSIS and Unbiased TCSIS. Finally, we demonstrate the effectiveness of TCSIS on problems from statistical physics.