Authors: Fred Zhangzhi Peng, Avishek Joey Bose, Anru R. Zhang, Alexander Tong
Organizations: Duke University · Imperial College London · AITHYRA
Abstract
Generative modeling over discrete structures underpins applications across deep learning, from biological sequence design and code generation to large language models, yet generation often remains sequential, relying on autoregressive decoding or iterative refinement. In this work, we introduce Coupling Models(Coupling Models), a one-step discrete generative model that learns a direct coupling between discrete sequences and Gaussian latents. Unlike recent distillation methods that compress a pretrained multi-step sampler into a few steps, Coupling Model trains a purpose-built decoder to invert this coupling and generate samples in a single step. The model also avoids complex continuous flows over the simplex and hand-specified data-to-noise couplings. Empirically,Coupling Model improves the strongest one-step baselines in each domain: it reduces LM1B text-generation perplexity by 33% at its lowest-perplexity operating point, Fly Brain enhancer-design FBD by 18%, and MNIST-Binary FID by 46%. These results suggest that effective one-step discrete generation depends strongly on how data and noise are coupled before decoding. Code is available at https://github.com/pengzhangzhi/Coupling-Models.
Discrete diffusion promises orders-of-magnitude faster generation than autoregressive (AR) models for sequential discrete data, yet its full potential of few-step generation has remained out of reach due to a fundamental structural limitation. The conditional-independence assumption underlying current discrete diffusion models introduces a systematic parallelization bias that compounds with the number of tokens unmasked per step, becoming severe in the few-step regime that fast generation requires. We address this with the first framework for explicit joint distribution modeling in discrete diffusion via tensor decomposition, which represents the conditional clean distribution as a low-rank tensor with controllable expressivity. The framework supports both Canonical Polyadic (CPD) and Tensor-Train (TTD) decompositions, and we identify a structural bias of TTD toward dependencies between nearby tokens, formalized through Oseledets' theorem relating TT-rank to unfolding-matrix rank, which is well-suited to sequential data such as natural language and line notations for molecular data. To enable efficient generation, we present an iterative marginal inference procedure with specialization for predetermined position schedules. Our framework integrates into pretrained MDMs through lightweight fine-tuning, yielding substantial improvements in few-step generation at a fraction of the cost of training from scratch.
Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn the target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we propose Forward-Learned Discrete Diffusion (FLDD), which introduces discrete diffusion with a learnable forward (noising) process. Rather than fixing a Markovian forward chain, we adopt a non-Markovian formulation with learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective. Experiments on various benchmarks show that, for a given number of sampling steps, our approach produces a higher quality samples than conventional discrete diffusion models using the same reverse parameterization.
Language generation is almost universally treated as a sequential process: autoregressive models emit one token at a time, while diffusion language models replace token-level seriality with a long trajectory of iterative refinement. In this work, we introduce PlaidQ, a 0.7B continuous diffusion language model for code generation, and show that its trajectory can be aggressively distilled into only a few denoising steps---or even one, enabling efficient code generation. PlaidQ repurposes a pretrained autoregressive model as a bidirectional denoiser over continuous token embeddings. We distill PlaidQ with distribution matching for few-step generation and paired-trajectory supervision for one-step generation. At matched model scale, PlaidQ is competitive with discrete diffusion language models on code generation. Distillation then shifts the quality--compute frontier: a 16-step student reaches 31.78 and 40.49 pass@10 on HumanEval and MBPP+, surpassing the same PlaidQ teacher sampled for 512 steps. At the extreme, paired-trajectory distillation achieves 7.07 pass@1 on HumanEval with a single denoising step, producing functionally correct programs. Together, these results establish continuous diffusion as a viable path to few-step and one-step code generation. Broadly, continuous diffusion is not merely another representation for language: it provides an interface through which language models can inherit the acceleration and distillation machinery of continuous diffusion modeling. Training and inference code and model checkpoints are available at https://github.com/pengzhangzhi/plaidq.