This work improves likelihood of score-based diffusion ODEs using high-order denoising score matching.
problem The gap between maximum likelihood and score matching objectives for score-based diffusion ODEs.
method High-order denoising score matching to maximize likelihood.
result Score-based diffusion ODEs achieve better likelihood on synthetic and CIFAR-10 data.
This work interprets diffusion score matching using normalizing flows for better model training and evaluations.
problem Limitations of diffusion score matching when dealing with certain types of distributions.
method The approach involves interpreting the diffusion matrix using normalizing flows to provide better interpretation and usage of diffusion score matching.
result Diffusion score matching is equivalent to the original score matching evaluated in the transformed space defined by the normalizing flow.
Automated denoising score matching handles nonlinear diffusion processes.
problem Nonlinear diffusion processes limit generative modeling and property estimation.
method Local-DSM using local increments and Taylor expansions.
result Tractable training and score estimation for nonlinear diffusion processes.
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.
Paper proposes a new method for training diffusion models using Markov operators.
problem Training efficiency and accuracy in diffusion models.
method Operator-informed score matching using spectral decomposition of Markov operators.
result Improved score matching for both low and high-dimensional distributions.
DDSME outperforms SME in estimating multimodal distributions.
problem Efficiency of score matching in multimodal distributions.
method Diffusion-based denoising score matching (DDSME) compared to vanilla score matching (SME).
result DDSME avoids the error bound deterioration of SME with increasing mode separation.
A new method for generating samples without training, using smoothed score matching.
problem Generating samples efficiently and without training.
method Moment-matched score-smoothed overdamped Langevin dynamics (MM-SOLD).
result The method enables fast, robust, training-free sampling with competitive sample fidelity and diversity.
A new method for training diffusion models using likelihood matching.
problem Training efficient and accurate diffusion models.
method Likelihood Matching approach, quasi-likelihood approximation, score and Hessian estimation.
result Consistent matching of first two transitional moments between diffusion steps.
WS diffusion models handle anisotropic Gaussian noise better than conventional methods.
problem Handling anisotropic Gaussian noise in imaging inverse problems.
method Whitened Score (WS) diffusion models based on stochastic differential equations.
result WS DMs outperform conventional DMs on anisotropic Gaussian noise.
New algorithm learns bridged diffusion processes without time-reversals.
problem Learning bridged diffusion processes efficiently and accurately.
method Score matching with Doob's h-transform, avoiding time-reversals.
result Outperforms existing methods in learning bridged diffusion processes.
PDDS samples from unnormalized densities using iterative particle scheme.
problem Sampling from unnormalized probability densities.
method Iterative particle scheme with novel score matching loss.
result Asymptotically consistent estimates for multimodal and high-dimensional tasks.
Method infers parameters in complex diffusion processes.
problem Parameter inference in high-dimensional, non-linear diffusion processes.
method Differentiable score matching to approximate diffusion bridges, used in an importance sampler.
result Numerically stable framework for parameter inference and diffusion mean estimation.
Theory explains creativity in diffusion models generating novel images.
problem Diffusion models generate highly original images far from training data.
method Identified locality and equivariance as inductive biases to prevent optimal score-matching.
result Analytic models predict diffusion model outputs with high accuracy.
Heuristic weighting improves denoising score matching without requiring noise distribution assumptions.
problem Improving denoising score matching without assuming noise distribution.
method Demonstrated heteroskedasticity, derived optimal weighting functions, and provided theoretical and empirical comparisons.
result Heuristical weighting function can achieve lower variance than optimal weighting, facilitating more stable and efficient training.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
New optimal rates for score estimation improve diffusion model performance.
problem Improving statistical rates for score estimation in diffusion models.
method Sharp minimax rates for score estimation of diffused distributions.
result Achieves sharp minimax rate without extraneous logarithmic terms.
New method boosts performance of diffusion models on discrete data like natural language.
problem Performance of diffusion models on discrete data like natural language is poor.
method Proposes score entropy, a novel loss that extends score matching to discrete spaces.
result Significantly boosts performance on language modeling tasks.
New method simulates diffusion bridges using score matching.
problem Simulating diffusion bridges for statistical inference.
method Backward time representation, variational formulation, score matching.
result Effective approximation of diffusion bridges.
Unified framework for denoising models across various spaces.
problem Improving generative models and approximate posterior simulation.
method Generalizing denoising diffusions to a broader class of spaces using a new extension of score matching.
result Unified models for denoising and posterior simulation.
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.
Score matching errors are not sufficient for measuring diffusion model quality.
problem The L2 score matching error is not a reliable measure of diffusion model performance. method Decomposed score errors into gradient and solenoidal components and analyzed their geometric properties.
result Only the gradient component of the score error affects the marginal distributional quality.
New score matching method estimates local intrinsic dimension efficiently.
problem Quantifying the local intrinsic dimension of complex data.
method Denoising score matching loss and equivalent implicit score matching loss.
result Denoising score matching loss is a highly competitive and scalable LID estimator.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
DDS samples from noisy data by reversing diffusion, providing theoretical guarantees.
problem Sampling from unnormalized densities.
method Denoising diffusion process, score matching, optimal control, Schrödinger bridges.
result DDS provides theoretical guarantees for sampling.
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
New geometric analysis shows L2 score error is flawed for diffusion models.
problem Score matching errors in diffusion models do not fully capture distributional quality.
method Decomposed score errors into gradient and solenoidal components, focusing on gradient's role in Fokker-Planck dynamics.
result Only gradient component affects marginal distributional quality; solenoidal component is structurally invisible.
Novel alignment framework for text-to-image generation using diffusion models and flow matching.
problem Improving text-to-image generation with minimal computational resources.
method Proposes a novel alignment framework that decomposes the score function into pre-trained score plus a conditional expectation of the reward.
result Achieves comparable performance to finetuning-based models with reduced computational cost.
Study shows how diffusion models learn on low-dimensional manifolds.
problem Learning efficiency of diffusion models on manifolds.
method Analyzes denoising score matching with random feature neural networks.
result Sample complexity scales linearly with intrinsic dimension, not ambient dimension.
Diffusion models adapt to data geometry through log-domain smoothing.
problem Understanding why diffusion models generalize well across diverse domains.
method Investigating the role of score matching and log-domain smoothing in diffusion models.
result Log-domain smoothing adapts the diffusion model to the data manifold.
SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
Improved diffusion models for generative tasks without dimensionality constraints.
problem Sample complexity bounds for learning score functions in diffusion models.
method Dimension-free sample complexity bounds, martingale-based error decomposition, variance reduction technique (Bootstrapped Score Matching).
result Achieved a double exponential improvement in sample complexity over prior results.
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
This work uncovers algorithm-dependent regularisation in diffusion models.
problem Understanding and improving generalisation in high-dimensional diffusion models.
method Algorithmic stability and score stability analysis.
result Identifies multiple sources of implicit regularisation unique to diffusion models.
Parallel score matching accelerates DPM training and improves density estimation.
problem Extended training periods and limited modeling flexibility in DPMs.
method Partitioning the learning task into independent time sub-intervals and modeling the score at each time point separately.
result Significant acceleration of training process and improved density estimation performance.
Improved score matching methods for estimating score functions and Hessians without high dimensionality.
problem Estimating score functions and Hessians efficiently in high-dimensional data.
method Implicit score matching and denoising score matching, leveraging Gagliardo-Nirenberg inequalities.
result Achieves convergence rates similar to denoising score matching and estimates Hessians without dimensionality issues.
SSDMs generate quantum states directly, outperforming classical methods.
problem Generating pure-state quantum representations efficiently.
method Score-based generative model on complex projective manifold.
result SSDMs match target pure-state ensembles by orders of magnitude.
Unified framework for training diffusion and flow models to sample from target distributions.
problem Training diffusion and flow models to sample from target distributions defined by exponential tilting.
method Unified framework combining stochastic optimal control and non-equilibrium thermodynamics perspectives.
result Unified bias-variance decompositions and theoretical support for adjoint-based methods.
Localized diffusion models reduce training complexity by exploiting low-dimensional structure.
problem Training diffusion models is computationally expensive due to the curse of dimensionality.
method Localized neural networks and localized score matching loss to estimate low-dimensional score functions.
result Localized diffusion models can circumvent the curse of dimensionality with reduced sample complexity.
Proposes CDTD, a diffusion model for mixed-type tabular data.
problem Adapting diffusion models to mixed-type tabular data.
method Score matching and score interpolation for continuous features, adaptive noise schedules for categorical features.
result Consistently outperforms state-of-the-art models in mixed-type tabular data.
New method calibrates DPMs to improve likelihood bounds.
problem Improving the likelihood bounds of DPMs.
method Deriving concentration bounds and using the optional stopping theorem for data scores to calibrate DPMs.
result Calibrated DPMs can increase likelihood bounds and improve sampling quality.
SDM Policy accelerates inference for robotic tasks while maintaining high action quality.
problem Prolonged inference times in diffusion-based policies for high-frequency control tasks.
method Two-stage optimization: score matching and distribution matching; dual-teacher mechanism.
result 6x inference speedup with state-of-the-art action quality.
New method modifies diffusions for singular rewards.
problem Handling singular rewards in diffusions.
method Malliavin calculus for non-differentiable rewards.
result Stable and reliable training of diffusions.
Grad-TTS models speech from text using diffusion probabilistic techniques.
problem Creating high-quality speech from text input.
method Score-based decoder with stochastic differential equations for noise-to-speech transformation.
result Grad-TTS produces mel-spectrograms from text input with competitive quality.
This paper conditions non-linear infinite-dimensional diffusion processes.
problem Conditioning non-linear and infinite-dimensional diffusion processes.
method Infinite-dimensional Girsanov's theorem to condition function-valued stochastic processes.
result Conditioning of non-linear infinite-dimensional diffusion processes is achieved.
Improved image generation quality using closed-form discriminator guidance in diffusion models.
problem Enhancing the quality of images generated by diffusion models.
method Theoretical framework to analyze GAN discriminator's effect on Langevin sampling, proposing IPM-GAN optimization as smoothed score-matching.
result Closed-form kernel-based discriminator guidance improves metrics like CLIP-FID and KID.
Diffusion models don't overfit, contrary to expectations.
problem Understanding generalization in diffusion models.
method Fundamental impossibility results and analysis of score matching.
result Diffusion models exhibit classical U-shaped loss curve, not double descent.
CTM improves diffusion model sampling quality with efficient ODE traversal.
problem Lack of natural trade-off between sample quality and speed in consistency models.
method CTM trains a neural network to output scores and traverse ODE trajectories efficiently.
result CTM achieves state-of-the-art FIDs and improves sample quality with increased computational budget.
We extend diffusion models to function spaces and introduce a new method for sampling from posterior distributions.
problem Sampling from posterior distributions in infinite-dimensional function spaces using diffusion models.
method Infinite-dimensional extension of Doob's h-transform, Supervised Guidance Training for efficient sampling. result We prove that diffusion models can be conditioned to sample from posterior distributions and introduce a simulation-free score matching objective.