Convergence Guarantees for Time-Inhomogeneous Uniform-Rate Discrete Diffusion Models

Discrete diffusion models have become an important class of generative models for categorical data, yet their theoretical understanding remains largely limited to time-homogeneous noise schedules. In this work, we study uniform-rate discrete diffusion models with time-inhomogeneous continuous-time Markov chain forward processes. We establish convergence guarantees for practical reverse-time samplers by directly controlling the total variation distance, avoiding the indirect route of first bounding KL divergence and then applying Pinsker's inequality. Our analysis decomposes the sampling error into initialization, score-estimation, discretization, and early-stopping errors, and explicitly characterizes how each term depends on the accumulated noise, the local noise rate, and the smoothness of the noise schedule. Under suitable regularity conditions on the noise schedule, we further derive step-complexity guarantees that match the order of existing results for homogeneous samplers.