One-Step Distillation of Discrete Diffusion Image Generators via Fixed-Point Iteration

Discrete diffusion models excel at visual synthesis but rely on slow, iterative decoding. Existing single-step distillation methods attempt to bypass this bottleneck, either by training auxiliary score networks that effectively double compute, or by introducing specialized parameterizations and multi-stage pipelines that fragment optimization. In this paper, we introduce Fixed-Point Distillation (FPD), an end-to-end framework that constructs local correction targets by partially corrupting the student's one-step draft and refining it with a single teacher step. To compute the training objective in a semantically meaningful space, we lift discrete tokens into continuous features and apply a multi-bandwidth drift loss that pulls the student toward these corrections. To backpropagate through the discrete bottleneck, we employ a straight-through estimator that decodes the exact hard-sampled tokens in the forward pass, ensuring that training and inference operate on the same codebook manifold, while routing continuous gradients back to the student logits. This fully differentiable pathway additionally accommodates an optional unconditional adversarial objective to enhance perceptual realism. Evaluations on both class-conditional and text-to-image generation validate the effectiveness of our framework. FPD achieves competitive visual fidelity and structural alignment against existing discrete distillation methods within only a single inference step.