Andrea Miele

Continuous diffusion language models involve two coupled design choices: how to corrupt continuous token representations and how to invert that corruption at generation time. Recent work has explored language generation on the unit sphere through geodesic and von Mises–Fisher (vMF) paths, raising the question of which forward process to use on this geometry and how much that choice matters relative to inference. We introduce Spherical Brownian Diffusion, using Brownian motion as the canonical isotropic diffusion on the sphere. Its heat semigroup provides a principled forward process, an additive dimension-free noise clock, and an exact ancestral bridge, while a clean-token posterior learned with cross-entropy supports multiple samplers. To separate corruption from inference, we derive high-dimensional approximation rates between Brownian and moment-matched vMF corruption and use this relationship for controlled substitutions. On Sudoku, Brownian and moment-matched vMF give nearly identical results across four samplers and five budgets under otherwise identical settings. In contrast, with the corruption process fixed, sampler choice produces a 25.0-point spread at a sampler budget of 180 calls. Using the ancestral bridge, we split this gain into a memory effect from re-noising the state, present on Sudoku and GSM8K, and a token-selection effect on GSM8K and largest at small budgets. Across reasoning tasks, categorical refinement improves performance, whereas unconditional text generation benefits from stochastic updates that preserve diversity.

Diffusion language models (dLLMs) promise fast inference by generating multiple tokens in parallel, but suffer severe performance degradation when parallel decoding is pushed too aggressively. We introduce Temporal Self-Distillation (TSD), a simple on-policy method that trains dLLMs for fast inference by distilling predictions across time. Specifically, TSD distills the model's denoising distribution at earlier timesteps toward its distribution at the final timestep at which a token is committed. This encourages earlier predictions to better anticipate the model's eventual output, enabling much more aggressive parallel decoding. Because its teacher signal comes from the model itself, TSD requires no offline teacher generation and applies seamlessly to both base and post-trained policies. Across seven benchmarks in mathematics, planning, and code, TSD substantially shifts the speed-quality frontier toward the low-compute regime. TSD thus provides a simple, single-stage approach to accelerating dLLMs, achieving speedups competitive with offline distillation while avoiding a complex two-stage pipeline.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, CoFRe. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8%, training time by 11.5%, and VRAM by 16.9%, while improving generative perplexity from 830.8 to 101.8 at a budget of 96 transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6% and VRAM by 50.7%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.