# Self-conditioned Flow Map Language Models via Fixed-point Flows

arXiv: https://arxiv.org/abs/2607.00714 · HTML: https://mlsanity.com/paper/2607.00714/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 30 of 36)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Likelihood-Based Diffusion Language Models](https://mlsanity.com/paper/2305.18619/) (2023)
- [The Diffusion Duality](https://mlsanity.com/paper/2506.10892/) (2025)
- [Self-conditioned Embedding Diffusion for Text Generation](https://mlsanity.com/paper/2211.04236/) (2022)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Beyond Autoregression: Fast LLMs via Self-Distillation Through Time](https://mlsanity.com/paper/2410.21035/) (2024)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [One-step Latent-free Image Generation with Pixel Mean Flows](https://mlsanity.com/paper/2601.22158/) (2026)
- [Distillation of Discrete Diffusion through Dimensional Correlations](https://mlsanity.com/paper/2410.08709/) (2024)
- [ELF: Embedded Language Flows](https://mlsanity.com/paper/2605.10938/) (2026)
- [Categorical Flow Maps](https://mlsanity.com/paper/2602.12233/) (2026)
- [LangFlow: Continuous Diffusion Rivals Discrete in Language Modeling](https://mlsanity.com/paper/2604.11748/) (2026)
- [CANDI: Hybrid Discrete-Continuous Diffusion Models](https://mlsanity.com/paper/2510.22510/) (2025)
- [Discrete Flow Maps](https://mlsanity.com/paper/2604.09784/) (2026)
- [Fixed-Point Reasoners: Stable and Adaptive Deep Looped Transformers](https://mlsanity.com/paper/2606.18206/) (2026)
- [Numerical Methods for Mean Field Games and Mean Field Type Control](https://mlsanity.com/paper/2106.06231/) (2021)
- [TEncDM: Understanding the Properties of the Diffusion Model in the Space of Language Model Encodings](https://mlsanity.com/paper/2402.19097/) (2024)
- [Language Modeling with Hyperspherical Flows](https://mlsanity.com/paper/2605.11125/) (2026)
- [Continuous Diffusion Scales Competitively with Discrete Diffusion for Language](https://mlsanity.com/paper/2605.18530/) (2026)

## Built on by (most cited first, 14 of 14)

- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (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)
- [Stochastic Flow Map for Count Data](https://mlsanity.com/paper/2609.23290/) (2026)
- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [Improving Few-Step Language Flows with Untied Self-Conditioning](https://mlsanity.com/paper/2608.22244/) (2026)
- [E-MoE: Enhanced Mixture-of-Experts for Non-Factorized Diffusion Language Models](https://mlsanity.com/paper/2609.37533/) (2026)
- [Gumbel Straight Flow: Distilling Autoregressive Models into One-step Flow Maps](https://mlsanity.com/paper/2610.00497/) (2026)
- [SOL: Measuring Gaps between Text Distributions by Double Sliced Wasserstein Metrics](https://mlsanity.com/paper/2610.06513/) (2026)
- [Representation-Space MMD for Diffusion Language Models](https://mlsanity.com/paper/2610.06648/) (2026)
- [Unrolled Flow Models for Reasoning](https://mlsanity.com/paper/2610.09759/) (2026)
- [On the Design Space of Continuous Diffusion Language Models](https://mlsanity.com/paper/2610.13834/) (2026)
- [Correction Training for Diffusion Models](https://mlsanity.com/paper/2610.14136/) (2026)
- [Coarse-Graining Recursive Expert Computation: Continuation-Relative Interfaces and Failure Modes](https://mlsanity.com/paper/2610.14413/) (2026)

## Abstract (arXiv)

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. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning perform a fixed-point iteration that improves generation through iterative refinement. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of self-conditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM^star, outperforms state-of-the-art self-conditioned models and few-step models in one- and few-step generation on OpenWebText. Code is available at https://github.com/Ugness/self-conditioned-fmlm.