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. Despite recent progress, 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. Our framework builds on masked diffusion and also extends to transport between pairs of distributions. We demonstrate that the resulting method scales effectively to high-dimensional systems, supports amortized sampling across different conditions, and enables accurate estimation of alloy phase diagrams.

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