Related papers: Discrete Diffusion Models: Novel Analysis and New …
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications and benefit from strong theoretical guarantees. Recently, methods inspired by statistical mechanics, in…
We propose Diffusion-Sharpening, a fine-tuning approach that enhances downstream alignment by optimizing sampling trajectories. Existing RL-based fine-tuning methods focus on single training timesteps and neglect trajectory-level alignment,…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…
When it is acknowledged that all candidate parameterised statistical models are misspecified relative to the data generating process, the decision maker (DM) must currently concern themselves with inference for the parameter value…
Langevin Dynamics is a Stochastic Differential Equation (SDE) central to sampling and generative modeling and is implemented via time discretization. Langevin Monte Carlo (LMC), based on the Euler-Maruyama discretization, is the simplest…
We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…
Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…
This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…
Discrete diffusion language models learn to reconstruct text from randomly masked inputs, yet under mild assumptions their denoiser already implements the exact Bayesian posterior over the original tokens. We prove that the expected…
Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…
Autoregressive language models, despite their impressive capabilities, struggle with complex reasoning and long-term planning tasks. We introduce discrete diffusion models as a novel solution to these challenges. Through the lens of subgoal…
Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…
The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…
We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of…
Anomaly detection is a fundamental task in machine learning and data mining, with significant applications in cybersecurity, industrial fault diagnosis, and clinical disease monitoring. Traditional methods, such as statistical modeling and…