Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation

• URL: http://arxiv.org/abs/2603.28572v1
• Date: Mon, 30 Mar 2026 15:26:56 GMT
• Title: Unrestrained Simplex Denoising for Discrete Data. A Non-Markovian Approach Applied to Graph Generation
• Abstract summary: We introduce simplex denoising, a simple yet effective generative framework that operates on the probability simplex.<n>For a given clean data point, noisy representations at different times are conditionally independent.<n> Empirically, emphunrestrained simplex denoising surpasses strong discrete diffusion and flow-matching baselines.
• Score: 50.328122325596865
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Denoising models such as Diffusion or Flow Matching have recently advanced generative modeling for discrete structures, yet most approaches either operate directly in the discrete state space, causing abrupt state changes. We introduce simplex denoising, a simple yet effective generative framework that operates on the probability simplex. The key idea is a non-Markovian noising scheme in which, for a given clean data point, noisy representations at different times are conditionally independent. While preserving the theoretical guarantees of denoising-based generative models, our method removes unnecessary constraints, thereby improving performance and simplifying the formulation. Empirically, \emph{unrestrained simplex denoising} surpasses strong discrete diffusion and flow-matching baselines across synthetic and real-world graph benchmarks. These results highlight the probability simplex as an effective framework for discrete generative modeling.

Related papers

• Search-Augmented Masked Diffusion Models for Constrained Generation [47.47350674873298]
  Search-Augmented Masked Diffusion (SearchDiff) is a training-free neurosymbolic inference framework that integrates informed search directly into the reverse denoising process.<n>SearchDiff substantially improves constraint satisfaction and property adherence, while consistently outperforming discrete diffusion and autoregressive baselines.
  arXiv  Detail & Related papers  (2026-02-02T19:43:25Z)
• Simple Denoising Diffusion Language Models [32.08084107137018]
  We propose a simplified denoising-based loss for Uniform-state Diffusion Models (USDMs)<n>We introduce a simple modification to our denoising loss with contrastive-inspired negative gradients, which is practical and yield additional improvements in generation quality.
  arXiv  Detail & Related papers  (2025-10-27T02:05:26Z)
• Deterministic Discrete Denoising [0.0]
  We propose a deterministic denoising algorithm for discrete-state diffusion models based on Markov chains.<n>The generative reverse process is derandomized by introducing a variant of the herding algorithm with weakly chaotic dynamics.<n>Our results reveal that deterministic reverse processes, well established in continuous diffusion, can also be effective in discrete state spaces.
  arXiv  Detail & Related papers  (2025-09-25T08:30:58Z)
• NoiseAR: AutoRegressing Initial Noise Prior for Diffusion Models [50.51982871889886]
  NoiseAR is a novel method for AutoRegressive Initial Noise Prior for Diffusion Models.<n>We formulate the generation of the initial noise prior's parameters as an autoregressive probabilistic modeling task over spatial patches or tokens.<n>Our experiments demonstrate that NoiseAR can generate initial noise priors that lead to improved sample quality and enhanced consistency with conditional inputs.
  arXiv  Detail & Related papers  (2025-06-02T05:32:35Z)
• Simple and Critical Iterative Denoising: A Recasting of Discrete Diffusion in Graph Generation [0.0]
  dependencies between intermediate noisy states lead to error accumulation and propagation during the reverse denoising process.<n>We propose a novel framework called Simple Iterative Denoising, which simplifies discrete diffusion and circumvents the issue.<n>Our empirical evaluations demonstrate that the proposed method significantly outperforms existing discrete diffusion baselines in graph generation tasks.
  arXiv  Detail & Related papers  (2025-03-27T15:08:58Z)
• Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions [1.9116784879310031]
  We introduce a new class of generative diffusion models that achieve a time-homogeneous structure for both the noising and denoising processes.<n>A key feature of the model is its adaptability to the target data, enabling a variety of downstream tasks using a pre-trained unconditional generative model.
  arXiv  Detail & Related papers  (2025-01-31T18:23:27Z)
• Robust Representation Consistency Model via Contrastive Denoising [83.47584074390842]
  randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations.<n> diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples.<n>We reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space.
  arXiv  Detail & Related papers  (2025-01-22T18:52:06Z)
• Sparse Training of Discrete Diffusion Models for Graph Generation [45.103518022696996]
  We introduce SparseDiff, a novel diffusion model based on the observation that almost all large graphs are sparse. By selecting a subset of edges, SparseDiff effectively leverages sparse graph representations both during the noising process and within the denoising network. Our model demonstrates state-of-the-art performance across multiple metrics on both small and large datasets.
  arXiv  Detail & Related papers  (2023-11-03T16:50:26Z)
• ChiroDiff: Modelling chirographic data with Diffusion Models [132.5223191478268]
  We introduce a powerful model-class namely "Denoising Diffusion Probabilistic Models" or DDPMs for chirographic data. Our model named "ChiroDiff", being non-autoregressive, learns to capture holistic concepts and therefore remains resilient to higher temporal sampling rate.
  arXiv  Detail & Related papers  (2023-04-07T15:17:48Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• From Denoising Diffusions to Denoising Markov Models [38.33676858989955]
  Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. We propose a unifying framework generalising this approach to a wide class of spaces and leading to an original extension of score matching.
  arXiv  Detail & Related papers  (2022-11-07T14:34:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.