Sampling from discrete, unnormalized distributions without access to data is a challenging problem. Neural samplers offer a promising approach by training generative models from density evaluations directly. However, existing discrete neural samplers are prone to mode collapse, come without convergence guarantees when trained via fixed-point iterations, and are often tied to a specific reference process such as masked or uniform diffusion. In this work, we introduce Discrete Gibbs Iterative Neural Sampler, a fixed-point neural sampler that addresses these limitations, enabling efficient, scalable learning, substantially reducing mode collapse in practice. Besides masked diffusion, the framework also extends to transport between arbitrary distributions. DIG-IN mitigates mode collapse on Ising and Potts models and scales to amortized sampling with up to 2,500 sites, recovers alloy phase diagrams, and learns to sample biomolecular Boltzmann distributions from energy alone. Its transport formulation accurately estimates solvation and conformational free energies. As a maximum-entropy RL policy, DIG-IN outperforms the Gaussian, diffusion, and flow policies we compare against across 20 continuous-control tasks.

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