New reweighted losses improve diffusion model training and image quality.
problem Training and improving diffusion models for image generation.
method Constructing a cascade of time-dependent variational lower bounds.
result Significant improvements in pixel-space image modeling quality.
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
Unified diffusive bounds for non-linear parabolic equations.
problem Proving diffusive upper bounds for parabolic equations.
method Simple exponential deformation argument.
result Unified diffusive upper bounds for a wide class of non-linear parabolic equations.
Discretizes diffusions and harmonic functions on covering spaces.
problem Harmonic functions on covering spaces with bounded growth.
method Lyons-Sullivan discretizations of diffusion operators.
result Equivalence of discretized and continuous harmonic functions.
New bounds show diffusion models converge nearly linearly in data dimension.
problem Improving convergence bounds for diffusion models.
method Refined discretization of reverse SDE using stochastic localization.
result Linear convergence in data dimension with logarithmic factors.
This work sets lower bounds on the number of score queries needed for diffusion sampling.
problem Establishing information-theoretic limits on the number of score evaluations required for diffusion sampling.
method Proving lower bounds on the number of adaptive score queries needed for sampling.
result Any sampling algorithm requires at least \(\widetilde{\Omega}(\sqrt{d})\) adaptive score queries for \(d\)-dimensional distributions.
DALMC provides non-asymptotic error bounds for generative models.
problem Efficiently generating samples from complex data distributions.
method Analysis of diffusion paths and Langevin Monte Carlo.
result Theoretical guarantees for a class of generative models.
Automates learning of multivariate diffusions for generative models.
problem Lack of automated methods for choosing and optimizing diffusion processes in generative models.
method Develops a recipe to maximize likelihood without model-specific analysis, parameterizes diffusion for target noise, and optimizes the inference diffusion process.
result Automatic search over all linear diffusions for generative models.
Algorithm learns diffusion processes with high-dimensional state spaces.
problem Stochastic control of unbounded diffusion processes with high-dimensional state spaces.
method Adaptive partitioning and learning algorithm that refines discretization based on estimation bias and statistical confidence.
result Established regret bounds that depend on problem parameters, extending to unbounded diffusion processes.
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower bound of order Ω ( k log p ) Ω(k \log p) Ω ( k log p ) , for directed graphs of p p p nodes, and at most k k k …
A new model combines diffusion and random features for better interpretability and comparable performance.
problem Lack of theoretical justification and computational expense in diffusion models, and limited interpretability in random feature models.
method Developed a deep random feature model inspired by diffusion models, derived generalization bounds using score matching.
result The model achieves comparable performance to fully connected neural networks and provides theoretical generalization bounds.
Score-based diffusion models achieve optimal error bounds under non-parametric assumptions.
problem Improving the minimax optimality of score-based diffusion models.
method Kernel-based score estimation and early stopping strategy.
result Achieves minimax optimal error bounds under sub-Gaussian and Sobolev space assumptions.
New risk bound for drift estimator in stochastic models.
problem Theoretical guarantees for drift estimation in stochastic differential equations.
method Derives an explicit risk bound using diffusion model theory.
result Explicit decomposition of risk into multiple sources of error.
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex …
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
An efficient algorithm for aligning diffusion trees to networks with information asymmetry.
problem Aligning diffusion trees to networks with information asymmetry.
method Tree correlation tests for extracting alignment information.
result Explicit lower bounds on the probability of correct matches for each vertex on the diffusion tree.
Improved sample complexity for training diffusion models.
problem How many samples are needed to train an accurate diffusion model?
method Analyzing the sample complexity of training diffusion models using neural networks.
result Exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other parameters.
Improved spectral convergence bounds for diffusion maps on tori.
problem Weak theoretical error bounds for diffusion maps.
method Spatial Hardy space estimates, PDE spectral stability, Sinkhorn weights.
result Matched pointwise error bounds for spectral data and operator convergence.
A method for diffusion on probability simplex for generative models.
problem Tension between continuous and discrete data in diffusion models.
method Proposes using softmax function applied to Ornstein-Uhlenbeck Process on probability simplex.
result Method extends to bounded image generation.
The paper analyzes statistical guarantees for denoising reflected diffusion models.
problem The mismatch between theoretical design and implementation of diffusion models introduces issues in high-dimensional target data.
method The paper uses a reflected diffusion process as the driver of noise and establishes rates of convergence in total variation.
result The statistical guarantees for denoising reflected diffusion models match the minimax lower bound up to a polylogarithmic factor.
This work analyzes discrete diffusion models using stochastic integrals, providing error bounds and insights.
problem Error analysis for discrete diffusion models remains less understood.
method Proposes a comprehensive framework based on Lévy-type stochastic integrals.
result Obtains the first error bound for the τ τ τ -leaping scheme in KL divergence. New framework for discrete-state diffusion models reduces sample complexity.
problem Lack of theoretical understanding and sample complexity analysis for discrete-state diffusion models.
method Developed a principled theoretical framework, decomposing score estimation error.
result Established sample complexity bound of O ~ ( ε − 2 ) \widetilde{\mathcal{O}}(ε^{-2}) O ( ε − 2 ) . We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized Γ Γ Γ -calculus techniques. The advantages and drawbacks of each of these methods are discussed.
Sharp statistical theory for conditional diffusion models.
problem Lack of theoretical foundation for conditional diffusion models.
method Sharp statistical theory with approximation of conditional score function.
result Sample complexity bound that adapts to data distribution smoothness.
We identify 'critical windows' in diffusion models where specific features emerge, providing a theoretical framework.
problem Understanding narrow time intervals in diffusion models where specific features emerge.
method Developed a formal framework to study these critical windows, showing provable bounds for certain data types.
result Proved that critical windows can be bounded in terms of measures of separation for data from mixtures of log-concave densities.
This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.
problem Theoretical guarantees for discrete-state diffusion models remain under-explored.
method Continuous Time Markov Chain (CTMC) framework and discrete-time sampling algorithm.
result Convergence bounds for KL divergence and TV distance are derived, showing linear dependence on dimension.
High-quality image synthesis with diffusion models, achieving state-of-the-art FID score.
problem Generating high-quality images from latent variables.
method Training diffusion probabilistic models with a weighted variational bound, inspired by denoising score matching and Langevin dynamics.
result State-of-the-art FID score of 3.17 on CIFAR10 dataset.
New method infers diffusion equations from sparse data.
problem Statistical inference of diffusion equations from limited data.
method Neural network-based estimators for drift and diffusion tensor.
result Statistical convergence guarantees for Hölder continuous processes.
Neural Flow Diffusion Models improve diffusion models by learning flexible forward processes.
problem Fixed forward processes in diffusion models complicate reverse processes and increase inference costs.
method Introduces NFDM, a framework supporting flexible forward processes and a novel parameterization technique.
result Demonstrates strong performance in likelihood estimation and learning generative dynamics.
The paper analyzes diffusion condensation for data geometry and topology.
problem Understanding the geometry and topology of high-dimensional data.
method Time-inhomogeneous diffusion process with geometric, spectral, and topological analysis.
result The condensation process defines intrinsic condensation homology and ambient persistent homology.
A new diffusion model tackles brightness issues with a probabilistic approach.
problem Brightness-related limitations in diffusion models.
method Introduces a novel diffusion model with a probabilistic framework, modifying both forward and reverse diffusion processes.
result The model mitigates brightness-related limitations and improves performance in high-dimensional settings.
Improved graph neural network bounds using graph diffusion matrix.
problem Empirical performance of graph neural networks on real-world graphs.
method Unified model of graph neural networks, focusing on feature diffusion matrix stability.
result Generalization bounds scale with largest singular value of feature diffusion matrix, smaller than prior bounds.
Conditional diffusion models improve data generation with non-asymptotic convergence bounds.
problem Lack of non-asymptotic properties in conditional diffusion models.
method Integrates a pre-trained model into the diffusion model framework to capture conditional distributions.
result Established upper error bounds for the convergence between original and generated conditional distributions.
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time T T T for multi-modal data distributions. A coupling method and an analytic one allow us to prove new lower bounds for the spectral gap of reversible diffusions on compact manifolds. Those bounds are based on the a notion of curvature of the diffusion, like the coarse Ricci curvature or the Bakry--Emery curvature-dimension inequalities. We show that when this …
Unified discrete diffusion for categorical data simplifies training and sampling.
problem Training and sampling in discrete diffusion models for categorical data.
method Mathematical simplifications and elegant unification of discrete-time and continuous-time discrete diffusion.
result Unified Simplified Discrete Denoising Diffusion (USD3) outperforms SOTA baselines.
Study error bounds and optimal schedules for Masked Diffusions with factorized approximations.
problem Analyzing trade-offs between computation and accuracy in Masked Diffusion Models.
method Provided general error bounds and identified optimal schedules based on data distribution information profiles.
result Identified optimal schedule sizes for Masked Diffusion Models.
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…
NDMs enable non-linear transformations in diffusion models for better generative tasks.
problem Limited to linear transformations, diffusion models struggle with generative tasks.
method Presented NDMs that allow time-dependent non-linear transformations.
result NDMs outperform conventional diffusion models in likelihood and sample quality.
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
Let L = Δ − ∇ φ ⋅ ∇ L=Δ-\nabla\varphi\cdot\nabla L = Δ − ∇ φ ⋅ ∇ be a symmetric diffusion operator with an invariant measure d μ = e − φ d x dμ=e^{-\varphi}dx d μ = e − φ d x on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with ∣ ∇ φ ∣ ≤ θ |\nabla \varphi|\leqθ ∣∇ φ ∣ ≤ θ and ∞ \infty ∞ -dimensional Bakry-Émer…
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
Study finds conditions for global minimizers on curved manifolds with fast diffusion and nonlocal interactions.
problem Existence of global minimizers for a free energy functional on negatively curved manifolds.
method Investigation of Carlson-Levin type inequalities for Cartan-Hadamard manifolds.
result Establishes necessary and sufficient conditions for the existence of global energy minimizers.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
We prove an upper bound on the bottom of the essential spectrum of a diffusion in term of the growth of the volume of X X X , generalizing a result by R. Brooks.
Improved KL convergence bounds for score diffusion models without restrictive assumptions.
problem Lack of comprehensive quantitative results for diffusion models, especially in non-regular scores and estimators.
method Score diffusion models with fixed step size from Ornstein-Uhlenbeck and kinetic semigroups, providing explicit and sharp KL convergence bounds.
result Explicit and sharp convergence bounds in KL applicable to any data distribution with finite Fisher information.
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using L 2 L^2 L 2 loss and regularity conditions. The paper analyzes sampling and estimation on manifolds using Langevin diffusion.
problem Sampling and estimation on compact Riemannian manifolds.
method Discretization of Langevin diffusion with error bounds derived.
result First-order error bounds for bias and variance in estimators.