Optimizers for Diffusion Models: A Controlled Benchmark

Diffusion language models are a promising alternative to autoregressive models due to their potential for faster generation. Among discrete diffusion approaches, Masked diffusion currently dominates, largely driven by strong perplexity on language modeling benchmarks. In this work, we present the first scaling law study of uniform-state and interpolating discrete diffusion methods. We also show that Masked diffusion models can be made approximately 12% more FLOPs-efficient when trained with a simple cross-entropy objective. We find that perplexity is informative within a diffusion family but can be misleading across families, where models with worse likelihood scaling may be preferable due to faster and more practical sampling, as reflected by the speed-quality Pareto frontier. These results challenge the view that Masked diffusion is categorically the future of diffusion language modeling and that perplexity alone suffices for cross-algorithm comparison. Scaling all methods to 1.7B parameters, we show that uniform-state diffusion remains competitive on likelihood-based benchmarks and outperforms autoregressive and Masked diffusion models on GSM8K, despite worse validation perplexity. We provide the code, model checkpoints, and video tutorials on the project page: http://s-sahoo.github.io/scaling-dllms

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2

Diffusion language models (dLLMs) have emerged as a promising alternative to autoregressive (AR) language models, offering flexible token-update orders and parallel decoding. Recent dLLMs are often initialized from pretrained AR models before diffusion conversion in order to inherit their learned representations. After the conversion, however, they typically ignore the extensive post-training ecosystem of their AR ancestors. In this work, we show that these existing AR post-training weight updates can instead be effectively recycled to enhance diffusion models. Despite the changes by AR-to-diffusion conversion, directly adding an AR post-training weight update to a diffusion base model remains effective, bringing its performance close to that achieved by direct diffusion post-training. Notably, AR and diffusion post-training updates are nearly orthogonal in weight space, yet induce substantially more aligned representation changes in the diffusion model. Their distinct updates are also complementary: composing their weights can retain gains from both regimes and further improve the post-trained diffusion model. Based on these findings, we propose A2D, a simple training-free framework for enhancing diffusion models with existing AR post-training resources. A2D can transfer capabilities from AR post-trained models to diffusion base models, and further improve already post-trained diffusion models by composing AR and diffusion post-training updates. Across various dLLMs, including Dream, DreamReasoner, DiffuCoder, Dream-Coder, Nemotron-Labs-Diffusion, and DiffusionGemma, A2D reliably improves instruction following, mathematical reasoning, and coding with both supervised fine-tuning and reinforcement learning updates, without additional training, or inference-time computation.