Discrete diffusion has emerged as a powerful framework for generative modeling in discrete domains, yet efficiently sampling from these models remains challenging. Existing sampling strategies often struggle to balance computation and sample quality when the number of sampling steps is reduced, even when the model has learned the data distribution well. To address these limitations, we propose a predictor-corrector sampling scheme where the corrector is informed by the diffusion model to more reliably counter the accumulating approximation errors. To further enhance the effectiveness of our informed corrector, we introduce complementary architectural modifications based on hollow transformers and a simple tailored training objective that leverages more training signal. We use a synthetic example to illustrate the failure modes of existing samplers and show how informed correctors alleviate these problems. On the text8 and tokenized ImageNet 256 256datasets, our informed corrector consistently produces superior samples with fewer errors or improved FID scores for discrete diffusion models. These results underscore the potential of informed correctors for fast and high-fidelity generation using discrete diffusion. Our code is available at https://github.

Generative models of graphs based on discrete Denoising Diffusion Probabilistic Models (DDPMs) offer a principled approach to molecular generation by systematically removing structural noise through iterative atom and bond adjustments. However, existing formulations are fundamentally limited by their inability to adapt the graph size (that is, the number of atoms) during the diffusion process, severely restricting their effectiveness in conditional generation scenarios such as property-driven molecular design, where the targeted property often correlates with the molecular size. In this paper, we reformulate the noising and denoising processes to support monotonic insertion and deletion of nodes. The resulting model, which we call GRIDDD, dynamically grows or shrinks the chemical graph during generation. GRIDDD matches or exceeds the performance of existing graph Diffusion Models on molecular property targeting despite being trained on a more difficult problem. Furthermore, when applied to molecular optimization, GRIDDD exhibits competitive performance compared to specialized optimization models. This work paves the way for size-adaptive molecular generation with graph diffusion.

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) - a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

Discrete diffusion models, like continuous diffusion models, generate high-quality samples by gradually undoing noise applied to datapoints with a Markov process. Gradual generation in theory comes with many conceptual benefits; for example, inductive biases can be incorporated into the noising Markov process, and access to improved sampling algorithms. In practice, however, the consistently best performing discrete diffusion model is, surprisingly, masking diffusion, which does not denoise gradually. Here we explain the superior performance of masking diffusion by noting that it makes use of a fundamental difference between continuous and discrete Markov processes: discrete Markov processes evolve by discontinuous jumps at a fixed rate and, unlike other discrete diffusion models, masking diffusion builds in the known distribution of jump times and only learns where to jump to. We show that we can similarly bake in the known distribution of jump times into any discrete diffusion model. The resulting models -- schedule-conditioned diffusion (SCUD) -- generalize classical discrete diffusion and masking diffusion. By applying SCUD to models with noising processes that incorporate inductive biases on images, text, and protein data, we build models that outperform masking.

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices.

ABSTRACT 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. 1 INTRODUCTION In the last years, diffusion models have demonstrated strong performance across many continuous (Hoogeboom et al., 2024) and discrete (Lou et al.) domains . Recent work has shown that distillation approaches and advanced training techniques allow learning a few-step (Salimans et al., 2024), or sometimes even a single-step, generative (Xu et al., 2025) procedure in the continuous domain.

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE, a generative model defined directly on relaxed incidence matrices via a structured stochastic diffusion. The forward process combines a hypergraph-specific two-sided heat operator with an Ornstein--Uhlenbeck component, preserving structure-aware noising near the data while yielding an explicit Gaussian terminal law. Conditional on an observed hypergraph, this forward process is linear-Gaussian, so conditional means, covariances, scores, and reverse-drift targets are available in closed form. We therefore learn a permutation-equivariant state-only reverse-drift field in incidence space by regressing onto exact conditional targets, and generate samples by simulating a learned reverse-time SDE from the Gaussian base law. We establish exactness in the ideal state-only setting together with finite-horizon stability guarantees, and empirically show improved hypergraph generation quality relative to strong baselines.

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Mises-Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.