Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning

• URL: http://arxiv.org/abs/2609.15903v2
• Date: Tue, 15 Sep 2026 14:23:01 GMT
• Title: Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning
• Abstract summary: We introduce Discrete Beckmann Transport Models (DBTM)<n>DBTM is built on a time-independent flow whose autonomous transport map provably carries any point in the ambient space to a fixed point in a single step.<n>On language modeling and reasoning tasks, DBTM enables one- and few-step generation that improves quality and accuracy over discrete diffusion and continuous flow baselines.
• Score: 1.6566972365776105
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Discrete diffusion and flow models are a promising alternative to autoregressive language models, but compressing many-step sampling into fewer steps typically requires distilling a pretrained teacher model. This caps the student at the teacher's quality and requires a costly two-stage training pipeline. We introduce Discrete Beckmann Transport Models (DBTM), built on a time-independent flow whose autonomous transport map provably carries any point in the ambient space to a fixed point on the vertices of the simplex in a single step. We show that this fixed-point property is characterized by a conservation equation whose residual can be minimized directly from data, removing the requirement for a teacher flow and time conditioning. Under this construction, a partially trained map corresponds to the flow truncated at finite time, so generation reduces to iterating one map until it reaches a fixed point. We further extend the map to a partial-context interpolant where additional function evaluations act as refinement steps rather than ODE integration steps. On language modeling and reasoning tasks, DBTM enables one- and few-step generation that improves quality and accuracy over discrete diffusion and continuous flow baselines.

Related papers

• Beckmann Transport Models: From Autonomous Flows to One-Step Maps [47.88178310873025]
  We propose an instantiation of flow matching that relies on a time-independent velocity field to map between two distributions.<n>We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation.
  arXiv  Detail & Related papers  (2026-08-03T04:45:52Z)
• Flow Map Learning via Nongradient Vector Flow [22.985676782036904]
  Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.<n>We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration.
  arXiv  Detail & Related papers  (2026-07-29T02:17:27Z)
• Perceptual Flow Matching for Few-Step Generative Modeling [64.26537634881244]
  Perceptual Flow Matching is a framework for few-step generation in flow-matching models.<n>We show that PFM produces high-quality few-step generators when supervised in an appropriate representation space.
  arXiv  Detail & Related papers  (2026-07-03T17:55:01Z)
• D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models [27.90064267850009]
  We propose D-OPSD, a novel training paradigm for step-distilled diffusion models.<n>D-OPSD enables the model to learn new concept, style, etc. without sacrificing the original few-step capacity.
  arXiv  Detail & Related papers  (2026-05-06T17:59:34Z)
• A Few-Step Generative Model on Cumulative Flow Maps [25.03991490159211]
  We propose a unified, few-step generative modeling framework based on emphcumulative flow maps for long-range transport in probability space.<n>At its core is a cumulative-flow abstraction that connects local, instantaneous, updates with finite-time transport.<n>We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation.
  arXiv  Detail & Related papers  (2026-05-05T10:51:40Z)
• FlowS: One-Step Motion Prediction via Local Transport Conditioning [3.883772843505009]
  Local transport conditioning makes one-step generative motion prediction practical for safety-critical autonomy.<n>FlowS achieves state-of-the-art Soft mAP (0.4804) and mAP (0.4703) with ensemble at 75, calibrated with single-step inference.
  arXiv  Detail & Related papers  (2026-04-28T19:06:06Z)
• FlowConsist: Make Your Flow Consistent with Real Trajectory [99.22869983378062]
  We argue that current fast-flow training paradigms suffer from two fundamental issues.<n> conditional velocities constructed from randomly paired noise-data samples introduce systematic trajectory drift.<n>We propose FlowConsist, a training framework designed to enforce trajectory consistency in fast flows.
  arXiv  Detail & Related papers  (2026-02-06T03:24:23Z)
• MeanFlowSE: one-step generative speech enhancement via conditional mean flow [13.437825847370442]
  MeanFlowSE is a conditional generative model that learns the average velocity over finite intervals along a trajectory.<n>On VoiceBank-DEMAND, the single-step model achieves strong intelligibility, fidelity, and perceptual quality with substantially lower computational cost than multistep baselines.
  arXiv  Detail & Related papers  (2025-09-18T11:24:47Z)
• Align Your Flow: Scaling Continuous-Time Flow Map Distillation [63.927438959502226]
  Flow maps connect any two noise levels in a single step and remain effective across all step counts.<n>We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks.<n>We show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.
  arXiv  Detail & Related papers  (2025-06-17T15:06:07Z)
• Truncated Consistency Models [57.50243901368328]
  Training consistency models requires learning to map all intermediate points along PF ODE trajectories to their corresponding endpoints.<n>We empirically find that this training paradigm limits the one-step generation performance of consistency models.<n>We propose a new parameterization of the consistency function and a two-stage training procedure that prevents the truncated-time training from collapsing to a trivial solution.
  arXiv  Detail & Related papers  (2024-10-18T22:38:08Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.