The paper introduces LAW (Loopholing All the Way), a continuous generative model that relies entirely on Self‑Conditioning (SC) to propagate expected embeddings across diffusion steps, decoding tokens only once at the end. LAW outperforms both discrete and continuous diffusion models on Sudoku, Maze, and TinyGSM benchmarks, achieving higher accuracy and solving a larger proportion of GSM8K problems. Fine‑tuning a pre‑trained Uniform Diffusion Model with LAW significantly boosts its performance, and on OpenWebText LAW approaches autoregressive models while maintaining a favorable Pareto frontier.
By Adrien Deschenaux, Nadezhda Ilieva, Justin Deschenaux, Manuel Madeira, Dorina Thanou, Aur\'elien Lucchi, Antonio Orvieto, Caglar Gulcehre, Pascal Frossard
arXiv:2607. 24507v1 Announce Type: cross Abstract: Existing methods mainly adapt pretrained autoregressive (AR) language models to masked diffusion, whereas we directly adapt them to uniform-noise diffusion, where every token remains editable during sampling.
By Xiaoyi Jiang, Jingyuan Li, Yixuan Jiang, Wei Liu, Yi Zhu, Zuoqiang Shi, Pipi Hu
The paper introduces Sigma, a large-scale continuous diffusion language model (3B/8B parameters) that uses steerable, low-dimensional ODE/SDE latent trajectories to address the non-smoothness of discrete diffusion models. Sigma is trained blockwise via likelihood optimization, jointly denoises Gaussian-corrupted token embeddings, and learns an optimal embedding geometry, leveraging pre-trained autoregressive weights for faster training. During inference, classifier-free guidance and score temperature are identified as essential for high-fidelity reasoning and coding, and Sigma matches or exceeds discrete models on benchmarks such as GSM8K, Minerva, HumanEval, MBPP, MATH-500, and AIME, while also revealing unique structural benefits like embedding-space steering and graceful degradation for low NFEs.
By Zhihan Yang, Wei Guo, Jean-Marie Lemercier, Simon Welker, Yonggan Fu, Mohammad Mahdi Kamani, Sajad Norouzi, Julius Berner, Tomas Geffner, Karsten Kreis, Yongxin Chen, Molei Tao, John Thickstun, Pavlo Molchanov, Ante Juki\'c, Arash Vahdat, Morteza Mardani
On-Policy Residual Learning for Diffusion Language Models (ORL) introduces a framework that learns residual context directly from model-generated trajectories, using an entropy-contraction objective to sharpen predictions. The approach co-designs algorithmic and system components—such as asynchronous residual capture, block-diffusion attention, and packed compute-balanced training—to enable practical scaling. Experiments on a 4B DLM converted from Qwen3-4B show up to 6.2× faster tokens per forward and 6.9× higher end-to-end throughput, while also improving speed-quality trade-offs over autoregressive models and transferring effectively to other DLMs like LLaDA-2.1-mini and DiffusionGemma.
By Yifan Yu, Yuqing Jian, Jisen Li, Yuezhou Hu, Tianyi Zhang, Xiaoxia Wu, Rui-Jie Zhu, Junxiong Wang, Zhongzhu Zhou, Fan Lai, James Zou, Chenfeng Xu
arXiv:2607. 03809v1 Announce Type: new Abstract: Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries.
By Benjamin Wiriyapong, Oktay Karakus, Can Eyupoglu, Kirill Sidorov
arXiv:2606. 10450v1 Announce Type: cross Abstract: DiffC provides a principled way to reuse pre-trained diffusion models for lossy compression, but its encoding and decoding procedures remain slow because they require many discretized forward and reverse steps.
By Fuma Kimishima, Jinjia Zhou
arXiv:2609.38364v1 Announce Type: cross
Abstract: Discrete diffusion models and flow matching have emerged as powerful frameworks for generative modeling over discrete state spaces, yet efficient few...
By Yidong Ouyang, Zhengyan Wan, Themis Haris, Tian Tan, Liqian Peng, Henry Li, Ziqian Lin, Jianhang Chen, Maryam Karimzadehgan, Alec Go, George Michailidis
The paper introduces Hierarchical Continuous Diffusion Language Models (H-CDLMs), a framework that jointly diffuses multiple token modalities—individual tokens and coarser clusters of token embeddings—to enhance continuous diffusion language models. Applied to the CoBit architecture, the resulting H-CoBit achieves significant empirical gains, improving MAUVE scores and achieving lower generative perplexity on LM1B and OWT, while also outperforming prior continuous diffusion models on GSM8K. The approach generalizes to other continuous generative paradigms, as shown by consistent improvements when applied to the flow matching model FLM.
By Mathias Ollu, Nikos Komodakis
The paper introduces ELF-REG, a scaling of continuous diffusion language models (dLMs) for reasoning tasks. By aligning representations and using a frozen autoregressive teacher to supervise intermediate denoiser features, ELF-REG achieves higher pass@1 rates on GSM8K, MATH-500, HumanEval, and MBPP compared to prior dLMs. The method also enables strong low‑NFE performance through early‑stop decoding of intermediate predictions.
By Zeyu Michael Li, William Xingxu Chen, Bingshuo Qian, Jiayin Liu, Xiang Cheng
The paper investigates two key design levers for Continuous Diffusion Language Models (CDLMs): self‑conditioning and embedding geometry. It shows that self‑conditioning mitigates a train/inference mismatch and can be implemented efficiently via a two‑level interpolant called DoubleCat, which significantly boosts TinyGSM accuracy. By adding discrete reveals to DoubleCat, the authors create SemiCat, achieving discrete‑diffusion‑level performance and outperforming discrete diffusion on several likelihood‑based benchmarks at 1.7B parameters. The study also finds that cross‑entropy training drives embeddings toward a geometry with decoding error rates comparable to one‑hot representations, and briefly explores additional options such as hybrid corruption processes and asynchronous noise schedules.
By Oscar Davis, Daan Roos, Alice Bizeul, Amitis Shidani, Victor Turrisi, Louis B\'ethune, Pierre Ablin, Marco Cuturi
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.
By Louis Grenioux, Maxence Noble
arXiv:2610.22543v1 Announce Type: new
Abstract: Diffusion language models (DLMs) promise parallel text generation, but in practice face an unresolved speed-quality trade-off. Exact decoding fills in...
By Eliezer Shlomi, Eliron Rahimi, Avi Mendelson, Chaim Baskin