Towards Closing the Autoregressive Gap in Language Modeling via Entropy-Gated Continuous Bitstream Diffusion

TL;DR

This paper introduces a novel continuous diffusion approach over binary bitstreams for language modeling, achieving state-of-the-art perplexity and efficiency, and bridging the gap with autoregressive models.

Contribution

It proposes modeling text as a continuous diffusion process over fixed-width binary bitstreams with entropy-gated stochastic sampling, improving performance and scalability.

Findings

Achieves a perplexity of 59.76 on LM1B with 130M parameters.

Establishes a new Pareto frontier on OpenWebText with fewer steps.

Removes vocabulary scaling bottleneck by predicting logit bits.

Abstract

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion approaches over token embeddings have narrowed this gap, suggesting continuous state spaces are highly effective for language. In this work, we further close the autoregressive gap by modeling text as a continuous diffusion process over fixed-width binary bitstreams. Our approach represents semantic tokens as analog bit sequences and utilizes a matched-filter residual parameterization to isolate contextual learning from analytic independent-bit posteriors. Crucially, we adopt a stochastic sampler that applies Langevin-type corrections gated by the entropy-rate profile, automatically concentrating stochasticity in high-information regions while remaining nearly deterministic elsewhere. On the One Billion Word Benchmark (LM1B), our 130M-parameter bitstream model reaches a generative perplexity ($\GenPPL$) of $59.76$ at matched real-data entropy ($4.31$) using 256 neural function evaluations (NFEs), decisively outperforming prior DLM baselines and reaching the autoregressive reference. On OpenWebText (OWT), our stochastic sampler establishes a new continuous-DLM Pareto frontier, achieving $\GenPPL=27.06$ at an entropy of $5.26$ using $4\times$ fewer steps than previous 1024-NFE baselines. As an additional architectural benefit, bitstream diffusion removes the $\mathcal{O}(V)$ vocabulary scaling bottleneck shared by standard DLMs. By predicting $\mathcal{O}(\log V)$ bitwise logits via semantic bit-patching, our model yields a reduced memory footprint and higher throughput, demonstrating a scalable paradigm for language generation as vocabulary sizes grow.