Discrete Beckmann Transport Models (DBTM) are introduced as a new type of discrete diffusion and flow model that can generate language in a single step by mapping any point to a fixed point on the simplex vertices. Unlike previous approaches, DBTM eliminates the need for a pretrained teacher model and time conditioning by minimizing a conservation equation directly from data. The model can be partially trained and iterated until convergence, and it can be extended to a partial‑context interpolant that refines outputs with additional function evaluations. Experiments on language modeling and reasoning tasks show that DBTM achieves higher quality and accuracy than existing discrete diffusion and continuous flow baselines.
By Sophia Tang, Shiyi Wang
arXiv:2605. 29920v2 Announce Type: replace Abstract: We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models.
By Daniil Shlenskii, Nikita Gushchin, Lev Novitskiy, Dmitry V. Dylov, Alexander Korotin
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
arXiv:2607. 27372v1 Announce Type: new Abstract: The deep learning revolution, kicked off by AlexNet, taught us that end-to-end training beats decomposing a problem into hand-designed stages.
By Alexi Gladstone, Heng Ji, Yilun Du
arXiv:2607. 00714v1 Announce Type: cross Abstract: Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate.
By Jaehoon Yoo, Wonjung Kim, Floor Eijkelboom, Chanhyuk Lee, Nicholas M. Boffi, Seunghoon Hong, Jinwoo Kim
High-fidelity image generation faces a trade-off between speed and quality. Diffusion models produce strong visuals but require costly iterative sampling.
arXiv:2607. 00535v1 Announce Type: cross Abstract: Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data.
By Zhiqi Li, Wen Zhang, Bo Zhu
arXiv:2605. 00941v4 Announce Type: replace Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem.
By Jiarui Xing, Song Wang, Jian Wang
The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.
By Alessandro Micheli, Andrea Zerio, Samir Bhatt
arXiv:2607. 21427v1 Announce Type: new Abstract: Discrete flow matching provides a flexible framework for generative modeling on discrete structures.
By Daniil Cherniavskii, Daniel Severo, Karen Ullrich
arXiv:2503. 07154v3 Announce Type: replace-cross Abstract: Generative pre-training is often framed through a false dichotomy between autoregressive models for discrete signals and diffusion models for continuous signals.
By Jiaming Song, Linqi Zhou
arXiv:2511. 09465v4 Announce Type: replace-cross Abstract: Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language models.
By Lukas Billera, Hedwig Nora Nordlinder, Jack Collier Ryder, Anton Oresten, Aron St{\aa}lmarck, Theodor Mosetti Bj\"ork, Ben Murrell