Slowly Annealed Jump Processes: Theory and Applications to MDM Fine-tuning

Annealing is a powerful strategy for sampling from complex distributions and reward-based fine-tuning of diffusion models, using a sequence of intermediate distributions to connect an easily sampled reference distribution to the desired target. However, if the target changes faster than the sampling or learning dynamics can adapt, substantial tracking error can persist. This motivates slow annealing, which gives the dynamics more time to adapt to the evolving target and recent work has established the effectiveness in both continuous-state sampling and guided generation. However, whether slow annealing yields comparable benefits for discrete jump processes and reward-based fine-tuning of masked diffusion models remains insufficiently understood. In this work, we develop a theory of slowly-annealed jump processes with forward KL tracking guarantees of slowly-annealed Glauber dynamics. We further derive conditional KL bounds for slowly-annealed masked diffusion fine-tuning under idealized learning dynamics. Experiments on tractable distributions and LLaDA-8B-Instruct demonstrate the benefits.