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

Research Question and Approach

Existing non-autoregressive language models face a fundamental trade-off: Masked Diffusion Models (MDMs) offer flexible, any-order generation but suffer from factorization errors that degrade quality when multiple tokens are generated simultaneously. Conversely, Flow Map Language Models (FMLMs) provide high-quality, few-step generation but lack the flexibility to perform iterative refinement. This paper introduces FMLM+, a unified framework that bridges these paradigms by equipping FMLMs with masking-style noise schedules. This architecture allows the model to generate full sequences while simultaneously scoring the global consistency of each token, enabling a novel inference-time strategy called Posterior Refinement (PR).

Posterior Refinement

Posterior Refinement is an iterative process where the model generates a draft sequence and then selectively retains only the tokens it is most confident in. Unlike traditional methods that rely on a-priori confidence (which often fails to account for global context), PR uses the model's final flow-map output to compute a-posteriori confidence scores. By evaluating how well each token fits into the globally generated sequence, the model can identify and erase incorrect tokens, regenerating them in subsequent rounds. This mirrors human cognitive processes of drafting, critiquing, and revising text.

Main Findings and Impact

FMLM+ establishes a new state-of-the-art in non-autoregressive language modeling, consistently outperforming both MDM and FMLM baselines across benchmarks like TinyStories, OpenWebText, GSM8K, and Sudoku. The authors demonstrate that by leveraging pretrained MDMs for initialization or distillation, FMLM+ converges faster and achieves higher accuracy. Most notably, the PR strategy allows the model to reach high-fidelity outputs with significantly fewer function evaluations (NFEs), offering a scalable and efficient foundation for future high-performance language generation systems.