Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data

• URL: http://arxiv.org/abs/2406.03736v2
• Date: Sat, 6 Jul 2024 14:40:08 GMT
• Title: Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data
• Authors: Jingyang Ou, Shen Nie, Kaiwen Xue, Fengqi Zhu, Jiacheng Sun, Zhenguo Li, Chongxuan Li,
• Abstract summary: We show that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data. We propose a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Our models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks.
• Score: 55.54827581105283
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Related papers

• Distillation of Discrete Diffusion through Dimensional Correlations [21.078500510691747]
  "Mixture" models in discrete diffusion are capable of treating dimensional correlations while remaining scalable. We empirically demonstrate that our proposed method for discrete diffusions work in practice, by distilling a continuous-time discrete diffusion model pretrained on the CIFAR-10 dataset.
  arXiv  Detail & Related papers  (2024-10-11T10:53:03Z)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation [6.9295879301090535]
  We propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic time series imputation. LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism.
  arXiv  Detail & Related papers  (2024-09-13T15:32:26Z)
• Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution [67.9215891673174]
  We propose score entropy as a novel loss that naturally extends score matching to discrete spaces. We test our Score Entropy Discrete Diffusion models on standard language modeling tasks.
  arXiv  Detail & Related papers  (2023-10-25T17:59:12Z)
• Denoising Diffusion Samplers [41.796349001299156]
  Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. We explore a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling.
  arXiv  Detail & Related papers  (2023-02-27T14:37:16Z)
• Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data [68.62134204367668]
  This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. The generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution.
  arXiv  Detail & Related papers  (2023-02-14T17:02:35Z)
• 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)
• Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance [95.12230117950232]
  We show that a common latent space emerges from two diffusion models trained independently on related domains. Applying CycleDiffusion to text-to-image diffusion models, we show that large-scale text-to-image diffusion models can be used as zero-shot image-to-image editors.
  arXiv  Detail & Related papers  (2022-10-11T15:53:52Z)

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.