Latent-Kernel Discrete Flow Maps (LKF), a from-scratch flow-map kernel that is a mixture of M factorized components tied by a single shared latent that learns strongly heterogeneous components and improves generative perplexity by 2.1x to 3.3x over the likelihood baselines without losing diversity.
Abstract
Discrete diffusion and flow-matching models denoise a sequence over many steps, but to keep each step cheap, they factorize the transition across positions and decide every token independently. This makes few-step generation challenging for text when the target couples two positions, such as a subject and a verb that must agree. An independent update commits to them separately, and many function evaluations are spent repairing the mismatch. Existing few-step methods buy back the lost correlation by distilling or rectifying a slow teacher, and so inherit the teacher's quality ceiling. We ask instead whether a model can express correlated steps natively, and answer with Latent-Kernel Discrete Flow Maps (LKF), a from-scratch flow-map kernel that is a mixture of M factorized components tied by a single shared latent. Conditioned on the latent, each component is cheap, and the mixture is summed over the latent in closed form for small M. We show that a single step places mass on correlated completions with the same sampling time complexity as a factorized model, since one latent is drawn per sequence and reused across the entire denoising trajectory. We also show that the Masked Diffusion Language Model (MDLM) is a special case of our LKF model at M=1. The experiments for unconditional text generation on the One-Billion-Word (LM1B) and WikiText-103 benchmarks show that our LKF model learns strongly heterogeneous components and improves generative perplexity by 2.1x to 3.3x over the likelihood baselines without losing diversity. The gain grows with M, and at M=8, it surpasses distilled and rectified few-step samplers. The source code is available at: https://github.com/mansoor181/lkf.git
Discrete diffusion and flow models are a promising alternative to autoregressive language models, but compressing many-step sampling into fewer steps typically requires distilling a pretrained teacher model. This caps the student at the teacher's quality and requires a costly two-stage training pipeline. We introduce Discrete Beckmann Transport Models (DBTM), built on a time-independent flow whose autonomous transport map provably carries any point in the ambient space to a fixed point on the vertices of the simplex in a single step. We show that this fixed-point property is characterized by a conservation equation whose residual can be minimized directly from data, removing the requirement for a teacher flow and time conditioning. Under this construction, a partially trained map corresponds to the flow truncated at finite time, so generation reduces to iterating one map until it reaches a fixed point. We further extend the map to a partial-context interpolant where additional function evaluations act as refinement steps rather than ODE integration steps. On language modeling and reasoning tasks, DBTM enables one- and few-step generation that improves quality and accuracy over discrete diffusion and continuous flow baselines.
This work empirically demonstrates that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood, and proposes a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information.
D. Cherniavskii, Daniel Severo, Karen Ullrich· arXiv.org· 0 citations
Diffusion language models (dLLMs) predict all tokens of a block in parallel, but a single forward pass samples each position from its own marginal distribution, so the tokens need not form a coherent block. We ask whether a discrete masked model can commit an entire block in one pass when its mask embeddings are perturbed by a sampled Gaussian noise field: the same noise should give the same coherent continuation, and different noise should give different ones. We propose CONDOR (Coupled-Noise Distillation for One-Step Readout), which trains such a model from scratch without a target-side encoder or an autoregressive teacher. Training combines two signals. On real text, the model predicts masked tokens under several noise samples and is supervised only through the sample that fits the ground truth best, so different noise can specialize to different continuations. For the remaining samples, the model refines its own one-pass prediction over several decoding steps under the same fixed noise and then distills that refined block back into a single pass. On a controlled TinyStories setting, this recipe yields coherent one-pass continuations that vary with the noise, both for a single block and, with a block-causal variant, when blocks are generated one after another.
It is shown that the mismatch degrades both the self-conditioning input and the solver update, and derive a correction for each from the model's own structure, and the resulting sampler, Untied Self-Conditioning, requires no retraining and uses one evaluation per step.
Simplax is introduced, an exact Dirichlet--categorical augmentation that couples each corrupted categorical state with an auxiliary simplex-valued variable while preserving the original uniform diffusion process as its categorical marginal.
Jinya Sakurai, Patrick Pynadath, Satoshi Hayakawa et al.· 1 citation
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.
Fred Zhangzhi Peng, Kai-Wen Zheng, An-Ru R. Zhang· 0 citations
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