The field of generative modeling is rapidly advancing, with a particular focus on diffusion models. Recent research has explored the use of information geometry to analyze diffusion models, revealing new insights into their behavior and properties. The development of novel sampling algorithms, such as Discrete Neural Flow Samplers and Split Augmented Langevin Sampling, has also improved the efficiency and effectiveness of generative models. Furthermore, researchers have investigated the use of physics-informed methods to enforce physical constraints on generated outputs, leading to more realistic and accurate results. Notably, papers such as 'Spacetime Geometry of Denoising in Diffusion Models' and 'Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation' have made significant contributions to the field by introducing innovative frameworks for analyzing and improving diffusion models. Additionally, 'Discrete Neural Flow Samplers with Locally Equivariant Transformer' has proposed a new approach to discrete sampling, and 'Test-Time Alignment of Discrete Diffusion Models with Sequential Monte Carlo' has introduced a method for aligning discrete diffusion models with sequential Monte Carlo methods.
Advances in Diffusion Models and Generative Modeling
Sources
Spacetime Geometry of Denoising in Diffusion Models
Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training
Discrete Neural Flow Samplers with Locally Equivariant Transformer
Distances for Markov chains from sample streams
Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling
Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensions
Backpropagation-Free Metropolis-Adjusted Langevin Algorithm
Efficient Diffusion Models for Symmetric Manifolds
Memorization to Generalization: Emergence of Diffusion Models from Associative Memory
Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation
Test-Time Alignment of Discrete Diffusion Models with Sequential Monte Carlo
Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study
Efficiently Access Diffusion Fisher: Within the Outer Product Span Space
Score-based Generative Modeling for Conditional Independence Testing
Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems
Optimization-Free Diffusion Model -- A Perturbation Theory Approach