Generating from Discrete Distributions Using Diffusions: Insights from Random Constraint Satisfaction Problems

ArXi:2603.20589v1 Announce Type: new Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for new generative techniques. In this paper, we show that fundamental insights from the theory of random constraint satisfaction problems have observable implications (sometime contradicting intuition) on the behavior of generative techniques on such benchmarks.