# Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flows

arXiv: https://arxiv.org/abs/2507.00425 · HTML: https://mlsanity.com/paper/2507.00425/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 81 references that are in the map.
- First posted on arXiv 1 Jul 2025.

## Builds on (most cited first, 30 of 67)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)

## Built on by (most cited first, 8 of 8)

- [Continuously Augmented Discrete Diffusion model for Categorical Generative Modeling](https://mlsanity.com/paper/2510.01329/) (2025)
- [Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization](https://mlsanity.com/paper/2510.08233/) (2025)
- [FARMER: Flow AutoRegressive Transformer over Pixels](https://mlsanity.com/paper/2510.23588/) (2025)
- [SimFlow: Simplified and End-to-End Training of Latent Normalizing Flows](https://mlsanity.com/paper/2512.04084/) (2025)
- [Latent Reasoning with Normalizing Flows](https://mlsanity.com/paper/2606.06447/) (2026)
- [Normalizing Flows with Iterative Denoising](https://mlsanity.com/paper/2604.20041/) (2026)
- [Distilled Continuous Diffusion Language Models Can Write Code in Few Steps---or One](https://mlsanity.com/paper/2609.04531/) (2026)
- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)

## Abstract (arXiv)

Autoregressive models have driven remarkable progress in language modeling. Their foundational reliance on discrete tokens, unidirectional context, and single-pass decoding, while central to their success, also inspires the exploration of a design space that could offer new axes of modeling flexibility. In this work, we explore an alternative paradigm, shifting language modeling from a discrete token space to a continuous latent space. We propose a novel framework TarFlowLM, that employs transformer-based autoregressive normalizing flows to model these continuous representations. This approach unlocks substantial flexibility, enabling the construction of models that can capture global bi-directional context through stacked, alternating-direction autoregressive transformations, support block-wise generation with flexible token patch sizes, and facilitate a hierarchical multi-pass generation process. We further propose new mixture-based coupling transformations designed to capture complex dependencies within the latent space shaped by discrete data, and demonstrate theoretical connections to conventional discrete autoregressive models. Extensive experiments on language modeling benchmarks demonstrate strong likelihood performance and highlight the flexible modeling capabilities inherent in our framework.