Categorical Drifting Models

We propose CatDrift, a categorical extension of Drifting Models for one-step generation in discrete spaces. We reinterpret drifting as a local alignment problem: each generated sample is corrected in the direction of a data-dependent field while remaining close to its current value. In the original formulation, this constraint is Euclidean, yielding additive updates in sample space. This choice is natural for continuous data but ill-suited to categorical variables, whose states lie on the simplex. Replacing the Euclidean penalty with a Bregman divergence turns the drifting update into a mirror-descent step, a standard object in optimization with a natural information-geometric interpretation. For negative entropy, the categorical update has a closed form: build a kernel-weighted positive-minus-negative field from real samples and the generator’s own outputs, add it to logits, project with softmax, and regress to the frozen target by cross-entropy. The result is a simple categorical drifting algorithm that obtains competitive-to-state-of-the-art one-step results on discrete image generation, molecular generation, and DNA sequence generation, without distilling diffusion models.