Researchers have introduced a post-training method for diffusion language models (DLMs) that minimizes Maximum Mean Discrepancy (MMD) between generated and reference distributions in the feature space of a frozen pretrained DLM. The approach is described in a paper titled Representation-Space MMD for Diffusion Language Models.
To estimate MMD, the method retains contextual features at individual token positions, yielding multiple observations per sequence from a single extractor pass. This design avoids the need for full sampling trajectories or jointly trained auxiliary models, which the authors note enables efficient post-training.
Optimization differs by model type: policy gradients are used for discrete models, while continuous models are optimized through direct differentiation with respect to generated latents. In both cases, the loss is computed directly from the retained features.
Experiments report lower generative perplexity at comparable entropy on OpenWebText and improved accuracy-computation trade-offs on GSM8K. On 16B DMax-LLaDA2.0 models with hybrid masked-uniform diffusion, the method increased decoding parallelism while maintaining similar or higher accuracy on math and code benchmarks.