# Posterior Refinement: Fast Language Generation via Any-Order Flow Maps

arXiv: https://arxiv.org/abs/2606.24773 · HTML: https://mlsanity.com/paper/2606.24773/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 59 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 30 of 48)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [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)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [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)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Dream 7B: Diffusion Large Language Models](https://mlsanity.com/paper/2508.15487/) (2025)
- [Taming Throughput-Latency Tradeoff in LLM Inference with Sarathi-Serve](https://mlsanity.com/paper/2403.02310/) (2024)
- [Non-Autoregressive Neural Machine Translation](https://mlsanity.com/paper/1711.02281/) (2017)
- [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)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Mercury: Ultra-Fast Language Models Based on Diffusion](https://mlsanity.com/paper/2506.17298/) (2025)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Masked Diffusion Models are Secretly Time-Agnostic Masked Models and Exploit Inaccurate Categorical Sampling](https://mlsanity.com/paper/2409.02908/) (2024)

## Built on by (most cited first, 11 of 11)

- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Discrete Beckmann Transport Models for One-Step Language Modeling and Reasoning](https://mlsanity.com/paper/2609.15903/) (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)
- [Reasoning with Continuous Latent Diffusion](https://mlsanity.com/paper/2609.35694/) (2026)
- [Alpha Diffusion Language Models: Factorization Alone Is Not the Problem](https://mlsanity.com/paper/2609.38066/) (2026)
- [Gumbel Straight Flow: Distilling Autoregressive Models into One-step Flow Maps](https://mlsanity.com/paper/2610.00497/) (2026)
- [Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Models](https://mlsanity.com/paper/2610.00894/) (2026)
- [Representation-Space MMD for Diffusion Language Models](https://mlsanity.com/paper/2610.06648/) (2026)
- [On the Design Space of Continuous Diffusion Language Models](https://mlsanity.com/paper/2610.13834/) (2026)
- [Next-Concept Modeling: Fast, Parallel Coarse-to-Fine Text Generation](https://mlsanity.com/paper/2610.14162/) (2026)

## Abstract (arXiv)

Non-autoregressive generation offers a powerful paradigm for iterative refinement, allowing models to recursively critique, erase and regenerate arbitrary subsets of tokens. However, existing non-autoregressive models fail to realize this potential. Masked Diffusion Models (MDMs) suffer from factorization error, causing sample quality to collapse when generating multiple tokens simultaneously. Flow Map Language Models (FMLMs) circumvent this bottleneck via joint sequence transport for excellent few-step generation, but sacrifice the inference-time flexibility of MDMs. We introduce FMLM+, a framework that bridges this gap by equipping FMLM with masking-style noise schedules. While generating the full sequence in a single step, FMLM+ simultaneously scores the global consistency of each token a posteriori. We leverage this to introduce Posterior Refinement, a novel inference-time refinement strategy that enables the model to adaptively self-correct its outputs, matching the performance of discrete baselines with 32x fewer NFEs. Across diverse benchmarks, we demonstrate that FMLM+ with Posterior Refinement improves the speed--quality tradeoff over both MDM and FMLM families, providing a scalable foundation for high-fidelity language modeling.