A hybrid randomized smoothing method yields a closed-form certificate for joint discrete-continuous perturbations that generalizes prior Gaussian and discrete smoothing approaches.
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Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution
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abstract
Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by $25$-$75$\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around $6$-$8\times$ better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with $32\times$ fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).
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representative citing papers
Derives an exact unbiased policy gradient for RL post-training of diffusion LLMs via entropy-guided step selection and one-step denoising rewards, achieving state-of-the-art results on coding and logical reasoning benchmarks.
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MDU minimizes forward KL divergence from prompt-conditional to prompt-masked unconditional predictions at masked positions to unlearn knowledge in MDLMs while trading off privacy and utility via temperature scaling.
FLDD learns non-Markovian marginal and posterior distributions for the forward process so a factorized reverse process can match the target better and produce higher-quality samples in fewer steps.
Discrete diffusion models learn data support before frequencies because the exact reverse process decomposes edits into a dominant validity scale and a finer probability coefficient.
JEDI is the first online end-to-end latent diffusion world model that trains latents from denoising loss rather than reconstruction, achieving competitive Atari100k results with 43% less VRAM and over 3x faster sampling than pixel diffusion baselines.
TABOM is a trajectory-aligned Boltzmann modeling framework that turns self-distilled inference paths into a pairwise ranking loss to close the training-inference gap in diffusion language models and expand their effective capabilities.
Introduces Block-R1 benchmark, Block-R1-41K dataset, and a conflict score to handle domain-specific optimal block sizes in RL post-training of diffusion LLMs.
Adaptive guidance trajectories learned via PPO outperform fixed-scale CFG on controllability-quality balance in three controlled NLP generation tasks with discrete diffusion models.
Diffusion language models develop early-layer collapse around an indispensable super-outlier due to overtraining, resulting in higher compressibility and reversed optimal sparsity patterns versus autoregressive models.
GD4 is a graph-based discrete denoising diffusion method for MIMO detection that yields higher-quality suboptimal solutions than prior diffusion detectors and classical baselines under similar compute budgets in both under- and over-determined settings.
StyleShield uses flow matching in continuous token embeddings with a DiT backbone to achieve 94.6% evasion on trained detectors and over 99% on unseen ones in Chinese benchmarks, with 0.928 semantic similarity, plus a RateAudit method to arbitrarily control detection rates.
Dream-Cubed releases a billion-scale voxel dataset and 3D diffusion models that generate controllable Minecraft worlds by operating directly on blocks.
NI Sampling accelerates discrete diffusion language models up to 14.3 times by training a neural indicator to select which tokens to sample at each step using a trajectory-preserving objective.
LangFlow is the first continuous diffusion language model to rival discrete diffusion on perplexity and generative perplexity while exceeding autoregressive baselines on several zero-shot tasks.
Full-sequence masking in SFT unlocks prompt infilling for masked diffusion language models, producing templates that match or surpass hand-designed ones and transfer across models.
MemDLM embeds a simulated denoising trajectory into DLM training via bi-level optimization, creating a parametric memory that improves convergence and long-context performance even when the memory is dropped at test time.
Diffusion language models form more global representations with early-layer redundancy compared to autoregressive models, allowing layer skipping for up to 18.75% FLOP savings while maintaining over 90% performance.
Early and late denoising steps in masked diffusion LMs are robust to smaller-model replacement, enabling 17% FLOPs reduction with modest generative quality loss.
CCDD defines a joint multimodal diffusion on continuous representation space and discrete token space to combine expressivity with explicit token supervision for diffusion language models.
Fast-dLLM adds reusable KV cache blocks and selective parallel decoding to diffusion LLMs, closing most of the speed gap with autoregressive models without retraining.
Smoothie performs diffusion by smoothing token embeddings based on semantic similarity, outperforming prior diffusion models on sequence-to-sequence and unconditional text generation tasks.
GRDM jointly generates relational database tables via graph-conditional diffusion without table ordering, outperforming autoregressive baselines on multi-hop correlations and single-table fidelity across six real RDBs.
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Thinking Diffusion: Penalize and Guide Visual-Grounded Reasoning in Diffusion Multimodal Language Models
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