Random Remasking Scales Masked Diffusion Inference

Masked diffusion models (MDMs) generate sequences by progressively unmasking tokens, but errors introduced during decoding are typically irreversible. Recent work has shown that iterative correction can improve sample quality, yet existing theory fails to explain this given a learned, imperfect denoiser model. We re-formulate MDM inference as a Markov chain on the clean sequence space, defined by a remask-denoise kernel that randomly re-introduces masks and then denoises. This helps us analyze the actual denoising trajectory, and we examine conditions under which each iteration step contracts the KL divergence. The analysis motivates Random Remask-Denoise (R${}^2$D) inference, a purely test-time, finetuning-free, reward-free procedure. To further improve performance, we propose Trajectory Correction Training (TCT), a denoiser-training procedure that exposes the model to its own errors along the generation trajectory. On logical tasks, our approach exhibits a striking near-log-linear test-time scaling, achieving over 97% accuracy on hard Sudoku puzzles and over 99% accuracy on 3-SAT. Our approach also applies to pretrained models on actual language tasks, beating iterative correction baselines and the official Q-mode accuracy of LLaDA2.1-mini on HumanEval+.