Discrete diffusion sampling stops rerolling at every jump: exponential residual flows make the trajectory deterministic after initialization and enable consistency distillation
Sampling from discrete diffusion models previously redrew randomness at every step, so the trajectory could not be fixed. Exponential residual flows give each position and token a continuous residual variable that evolves deterministically by piecewise ODEs after initialization, with a token change triggered whenever a residual reaches zero, and the construction is proved to preserve the marginals of the original diffusion at every time. At matched model-evaluation budgets, generation quality is comparable to ancestral sampling, and the deterministic trajectories support consistency distillation.