Autoregressive Models Rival Diffusion Models at ANY-ORDER Generation

Diffusion language models enable any-order generation and bidirectional conditioning, offering appealing flexibility for tasks such as infilling, rewriting, and self-correction. However, their formulation—predicting one part of a sequence from another within a single-step dependency—limits modeling depth and often yields lower sample quality and stability than autoregressive (AR) models. To address this, we revisit autoregressive modeling as a foundation and reformulate diffusion-style training into a structured multi-group prediction process. We propose Any-order Any-subset Autoregressive modeling (A3), a generalized framework that extends the standard AR factorization to arbitrary token groups and generation orders. A3 preserves the probabilistic rigor and multi-layer dependency modeling of AR while inheriting diffusion models' flexibility for parallel and bidirectional generation. We implement A3 through a two-stream attention architecture and a progressive adaptation strategy that transitions pretrained AR models toward any-order prediction. Experiments on question answering, commonsense reasoning, and story infilling demonstrate that A3 outperforms diffusion-based models while maintaining flexible decoding. This work offers a unified approach for a flexible, efficient, and novel language modeling paradigm. Code is at https://github.com/PKU-ML/Any-order-Any-subset-AR.