# Logit-KL Flow Matching: Non-Autoregressive Text Generation via Sampling-Hybrid Inference

arXiv: https://arxiv.org/abs/2411.16821 · HTML: https://mlsanity.com/paper/2411.16821/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 24 of its 35 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 24 of 24)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [SSD-LM: Semi-autoregressive Simplex-based Diffusion Language Model for Text Generation and Modular Control](https://mlsanity.com/paper/2210.17432/) (2022)
- [LaMini-LM: A Diverse Herd of Distilled Models from Large-Scale Instructions](https://mlsanity.com/paper/2304.14402/) (2023)
- [Self-conditioned Embedding Diffusion for Text Generation](https://mlsanity.com/paper/2211.04236/) (2022)
- [Dirichlet Flow Matching with Applications to DNA Sequence Design](https://mlsanity.com/paper/2402.05841/) (2024)
- [Step-unrolled Denoising Autoencoders for Text Generation](https://mlsanity.com/paper/2112.06749/) (2021)
- [Text Generation with Diffusion Language Models: A Pre-training Approach with Continuous Paragraph Denoise](https://mlsanity.com/paper/2212.11685/) (2022)
- [Fisher Flow Matching for Generative Modeling over Discrete Data](https://mlsanity.com/paper/2405.14664/) (2024)
- [DINOISER: Diffused Conditional Sequence Learning by Manipulating Noises](https://mlsanity.com/paper/2302.10025/) (2023)
- [Masked Audio Generation using a Single Non-Autoregressive Transformer](https://mlsanity.com/paper/2401.04577/) (2024)

## Built on by (most cited first, 1 of 1)

- [Sampling from Flow Language Models via Marginal-Conditioned Bridges](https://mlsanity.com/paper/2605.13681/) (2026)

## Abstract (arXiv)

Non-autoregressive (NAR) language models offer notable efficiency in text generation by circumventing the sequential bottleneck of autoregressive decoding. However, accurately modeling dependencies in discrete sequences remains challenging in this paradigm. In this work, we advance the field of NAR generation by applying conditional flow matching (CFM) methods grounded in geometrically principled interpolation, specifically leveraging Kullback-Leibler (KL) divergence geodesics, which correspond to linear interpolation in logit space. We rigorously establish that maximizing conditional likelihood in this setting precisely recovers the flow matching velocity field, supplying the theoretical justification for this approach in sequence modeling. To address practical performance gaps of basic inference, we propose a novel empirical sampling strategy that iteratively denoises and re-noises, along with a hybrid scheme that integrates our sampling method with basic procedure. Across unconditional and conditional text and code infilling, the approach improves perplexity and downstream metrics over prior NAR baselines under matched settings.