# PairFlow: Closed-Form Source-Target Coupling for Few-Step Generation in Discrete Flow Models

arXiv: https://arxiv.org/abs/2512.20063 · HTML: https://mlsanity.com/paper/2512.20063/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Builds on (most cited first, 29 of 29)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [One Billion Word Benchmark for Measuring Progress in Statistical Language Modeling](https://mlsanity.com/paper/1312.3005/) (2013)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Exploring the Limits of Language Modeling](https://mlsanity.com/paper/1602.02410/) (2016)
- [Simple Guidance Mechanisms for Discrete Diffusion Models](https://mlsanity.com/paper/2412.10193/) (2024)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [MaskBit: Embedding-free Image Generation via Bit Tokens](https://mlsanity.com/paper/2409.16211/) (2024)
- [Fine-Tuning Discrete Diffusion Models via Reward Optimization with Applications to DNA and Protein Design](https://mlsanity.com/paper/2410.13643/) (2024)
- [Beyond Autoregression: Fast LLMs via Self-Distillation Through Time](https://mlsanity.com/paper/2410.21035/) (2024)
- [Meissonic: Revitalizing Masked Generative Transformers for Efficient High-Resolution Text-to-Image Synthesis](https://mlsanity.com/paper/2410.08261/) (2024)
- [GenMol: A Drug Discovery Generalist with Discrete Diffusion](https://mlsanity.com/paper/2501.06158/) (2025)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Distillation of Discrete Diffusion through Dimensional Correlations](https://mlsanity.com/paper/2410.08709/) (2024)
- [textitJump Your Steps: Optimizing Sampling Schedule of Discrete Diffusion Models](https://mlsanity.com/paper/2410.07761/) (2024)
- [ReDi: Rectified Discrete Flow](https://mlsanity.com/paper/2507.15897/) (2025)

## Built on by (most cited first, 5 of 5)

- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [Kernel-Gradient Drifting Models](https://mlsanity.com/paper/2605.10727/) (2026)
- [Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusion](https://mlsanity.com/paper/2605.23346/) (2026)
- [Coupling Models for One-Step Discrete Generation](https://mlsanity.com/paper/2605.07193/) (2026)
- [One-Step Generation via Riemannian Wasserstein Gradient Flows](https://mlsanity.com/paper/2610.04454/) (2026)

## Abstract (arXiv)

We introduce textttPairFlow, a lightweight preprocessing step for training Discrete Flow Models (DFMs) to achieve few-step sampling without requiring a pretrained teacher. DFMs have recently emerged as a new class of generative models for discrete data, offering strong performance. However, they suffer from slow sampling due to their iterative nature. Existing acceleration methods largely depend on finetuning, which introduces substantial additional training overhead. textttPairFlow addresses this issue with a lightweight preprocessing step. Inspired by ReFlow and its extension to DFMs, we train DFMs from coupled samples of source and target distributions, without requiring any pretrained teacher. At the core of our approach is a closed-form inversion for DFMs, which allows efficient construction of paired source-target samples. Despite its extremely low cost, taking only up to 1.7% of the compute needed for full model training, textttPairFlow matches or even surpasses the performance of two-stage training involving finetuning. Furthermore, models trained with our framework provide stronger base models for subsequent distillation, yielding further acceleration after finetuning. Experiments on molecular data as well as binary and RGB images demonstrate the broad applicability and effectiveness of our approach.