GADD: Gibbs-Accelerated Discrete Diffusion Achieves Polylog Sampling Complexity
This paper introduces Gibbs-Accelerated Discrete Diffusion (GADD), a corrector method for uniform-rate discrete diffusion models that constructs Gibbs posterior likelihoods directly from the concrete score function without additional training. GADD achieves O(polylog(ε⁻¹)) sampling complexity, the first such rate for diffusion-based samplers in this setting. Experiments on synthetic data, zero-shot text sampling, and zero-shot conditional music generation show consistent improvements in sample quality and wall-clock efficiency over Euler and CTMC baselines. The work also introduces a novel induction-based theoretical framework for analyzing predictor-corrector methods in discrete diffusion.
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LESS: Adaptive mutual-stability sampling cuts diffusion LLM decoding steps by 72%
Researchers introduce LESS, a training-free adaptive sampler for diffusion large language models that treats token commitment as an online stopping problem. The method uses a joint stability rule combining confidence, persistence, and distributional stability to decide when to unmask tokens, avoiding wasted computation on already-stable positions. Evaluated on Dream-7B, LLaDA-8B, and LLaDA-1.5-8B across seven benchmarks, LESS reduces reverse denoising steps by 72.1% versus fixed-budget decoding while improving accuracy over prior adaptive samplers. The step reductions translate directly to fewer Transformer forward passes and lower wall-clock latency.
ADAS: Attention-Discounted Adaptive Sampler improves parallel decoding for masked diffusion language models
Researchers propose ADAS, a training-free reranking rule for masked diffusion language model decoding that addresses token interaction failures in parallel token commitment. The method greedily penalizes candidates that attend strongly to already-selected uncertain positions, using attention weights as soft marginal penalties rather than hard constraints. Evaluated on LLaDA-8B-Base and Dream-7B-Base across GSM8K, MATH500, HumanEval, and MBPP, ADAS improves low-NFE performance by 9–10 percentage points on average when plugged into existing samplers with only 3.1% runtime overhead.
Kolmogorov Regression lifts diffusion policies to Cameron-Martin space for robust long-horizon control
Researchers introduce a backward Kolmogorov equation framework that reformulates diffusion policy training as a deterministic boundary-value PDE problem in Cameron-Martin space, replacing stochastic score matching. The approach uses a precision-weighted Cameron-Martin loss and a Kolmogorov residual as an inference-time failure detector, yielding convergence guarantees tied to kernel effective rank rather than action dimension. Validation on the PushT manipulation benchmark shows 17% improvement in episode reward and 67.6% reduction in inter-step drift; a 6-station manufacturing scheduling task shows 28.4% lower RMSE than LSTM baselines and 96% reduction in deadlock events via Hamilton-Jacobi reachability certification.
MG-ADSGD achieves optimal communication complexity for decentralized stochastic strongly convex optimization
Researchers propose Multi-Gossip Accelerated DSGD (MG-ADSGD), a decentralized stochastic optimization algorithm that simultaneously achieves accelerated dependence on both the condition number (√κ) and the network spectral gap (1/√(1-β)), a combination no prior stochastic method had attained. The algorithm couples gossip depth with mini-batch size so that additional communication rounds improve both consensus accuracy and gradient variance reduction. The resulting communication complexity is claimed to be the best currently known for decentralized stochastic strongly convex optimization up to logarithmic factors.
Finite-Sample Lens for Understanding Diffusion Posterior Sampler Failures
This paper introduces a finite-sample theoretical framework for analyzing diffusion model posterior samplers used in imaging inverse problems. The authors show that popular likelihood approximations at intermediate timesteps systematically under- or over-estimate posterior spread, leading to failure modes including sensitivity to early stopping, incorrect weighting of posterior modes, and hallucination of prior or likelihood modes. Crucially, they demonstrate these failures can arise from a multimodal prior alone, without requiring nonlinear measurement models or multimodal posteriors. The framework is model-agnostic and can serve as a diagnostic tool for evaluating existing and future posterior samplers.
Exact Posterior Score (EPS): Closed-form posterior sampling for linear inverse problems with diffusion models
A new arXiv preprint derives the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, showing that posterior sampling reduces to a denoising problem at an operator-dependent shifted pivot under anisotropic noise covariance. The authors convert this identity into a training objective called Exact Posterior Score (EPS) that preserves the input/output structure of standard diffusion pretraining, enabling training from scratch or fine-tuning from a pretrained denoiser. EPS is evaluated on five linear inverse problems across FFHQ and ImageNet, outperforming both training-free and training-based baselines while requiring roughly an order of magnitude fewer denoiser evaluations than gradient-based posterior samplers.
SURGE: Approximation-free Training-Free Particle Filter for Diffusion Surrogate
The paper introduces URGE (Unbiased Resampling via Girsanov Estimation), a derivative-free inference-time scaling algorithm for diffusion models that performs path-wise importance reweighting using a Girsanov change of measure. Unlike existing inference-time guidance methods, URGE requires no score, Hessian, or PDE evaluations, attaching multiplicative weights to simulated trajectories and periodically resampling. The authors establish a theoretical equivalence between path-wise and particle-wise sequential Monte Carlo (SMC), guaranteeing unbiased terminal distributions. Empirically, URGE outperforms existing inference-time guidance baselines on synthetic tests and diffusion-model benchmarks while being simpler to implement.
RePlaid: Continuous Diffusion Language Models Scale Competitively with Discrete Diffusion
This paper revisits continuous diffusion language models (DLMs) by introducing RePlaid, an updated version of Plaid that aligns its architecture with modern discrete DLMs. RePlaid establishes the first scaling law for continuous DLMs competitive with discrete approaches, achieving a compute gap of only 20× versus autoregressive models and a state-of-the-art perplexity bound of 22.1 on OpenWebText among continuous DLMs. The authors provide theoretical analysis showing that likelihood-based training naturally yields linear cross-entropy over time and creates structured embedding geometries, explaining the performance gains.