BaM improves BBVI by optimizing a score-based divergence, leading to faster convergence.
problem Slow convergence of black-box variational inference methods.
method Batch and match (BaM) approach based on a score-based divergence.
result BaM converges exponentially quickly to the target mean and covariance.
New divergences improve score-based methods for multi-modal distributions.
problem Blindness problem in score-based divergences for multi-modal distributions.
method Proposed a new family of divergences to mitigate blindness.
result Improved performance in density estimation compared to traditional approaches.
Improved hypothesis testing and change-point detection using diffusion-based methods.
problem Limited power of score-based hypothesis tests and change-point detection.
method Extending score-based Fisher divergence to diffusion-divergence by multiplying score functions with a matrix-valued function or weight matrix.
result Theoretical quantification and demonstration of optimal performance of diffusion-based algorithms.
Researchers establish bounds for SGMs' KL and Wasserstein divergences under various noise schedules.
problem Estimating the error between target and estimated distributions in SGMs.
method Established upper bounds for KL divergence and Wasserstein distance, incorporating target distribution properties and SGM hyperparameters.
result Optimal noise schedules identified for SGMs, improving generative quality.
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.
New method samples from posterior distributions efficiently.
problem Posterior sampling in score-based models is intractable.
method Annealed Langevin Monte Carlo with KL and Fisher divergence.
result Tractable sampling from distributions close to posterior and prior.
Bi-Lipschitz flows approximate a wide range of distributions.
problem Characterizing the expressivity of bi-Lipschitz normalizing flows.
method Linking score regularity to transport map bi-Lipschitzness via probability flow ODE.
result Gaussian pullbacks induced by bi-Lipschitz variance-preserving transport maps are L1-dense among all probability densities. Improves BBVI for high-dimensional Gaussian approximations by using low-rank approximations.
problem Scalability issues with BBVI for high-dimensional multivariate Gaussian approximations.
method Extends BaM framework to handle full covariance matrices by integrating patch step for low-rank parameterization.
result Shows improved efficiency and scalability on synthetic and real-world high-dimensional inference problems.
New CUSUM algorithm detects changes in unnormalized models.
problem Change detection in models with unknown normalization constants.
method Score-based CUSUM (SCUSUM) algorithm based on Fisher divergence and Hyvärinen score.
result Asymptotic optimality of the SCUSUM algorithm demonstrated.
Unified framework for generating heavy-tailed distributions.
problem Extending SGMs to heavy-tailed targets.
method Combining early stopping with initialization for diffusion, and normalizing flows for generation.
result Unified generative framework with theoretical guarantees for heavy-tailed distributions.
MINDE estimates Mutual Information using neural diffusion models.
problem Estimating Mutual Information between random variables.
method Score-based diffusion models to estimate Kullback Leibler divergence.
result MINDE is more accurate than existing methods, especially for challenging distributions.
Generative models tackle incompressible fluid flows by enforcing divergence-free constraints.
problem Simulating incompressible fluid flows with generative models.
method Score-based diffusion models with divergence-free constraint.
result Models can reproduce Kolmogorov turbulence characteristics.
EigenVI uses orthogonal function expansions for efficient variational inference.
problem Efficiently approximate complex distributions in variational inference.
method EigenVI constructs variational approximations using orthogonal function expansions, minimizing Fisher divergence.
result EigenVI provides more accurate approximations than existing methods for Gaussian BBVI.
Paper analyzes convergence of DDPM for general distributions.
problem Theoretical understanding of DDPM's convergence properties remains limited.
method Introduced a relaxed smoothness condition and proved near-optimal convergence rates.
result Established a convergence rate of \( \widetilde{O}\left(\frac{d\min\{d,L^2\}}{T^2}
ight) \) in Kullback-Leibler divergence.
Paper analyzes Langevin dynamics for solving infinite-dimensional Bayesian inverse problems.
problem Solving high-dimensional Bayesian inverse problems in infinite-dimensional function spaces.
method Preconditioned Langevin dynamics with score-based generative models (SGMs).
result Derives error estimates and sufficient conditions for global convergence in Kullback-Leibler divergence.
VI struggles to fully quantify uncertainty when distributions don't factorize.
problem Uncertainty quantification in non-factorizable distributions.
method Analysis of variational inference trade-offs and divergence choices.
result Different divergences yield different measures of uncertainty in VI.
This paper improves SGMs by using a predictor-corrector scheme to converge faster.
problem Theoretical and practical limitations of existing SGMs when T1o∞. method Integrates a predictor-corrector scheme after the forward process to converge in finite time.
result Convergence guarantees for SGMs require only a fixed finite time T1. The paper analyzes how synthetic data training degrades diffusion models, providing bounds and characterizing different drift regimes.
problem The degradation of performance in diffusion models trained on synthetic data.
method Theoretical analysis of score-based diffusion models, focusing on the accumulated divergence between generated and target distributions.
result Upper and lower bounds on the accumulated divergence, providing the first lower bound for diffusion models.
The paper explores how information theory aids in statistical learning models.
problem Characterizing fundamental performance limits in statistical learning models.
method Introduces divergence measures and evidence lower bound (ELBO) in model training.
result Provides a systematic derivation for generative diffusion models.
VT-DIS improves sampling from Boltzmann distributions with minimal overhead.
problem Bias in Monte Carlo estimates from score-based diffusion models.
method Variance-Tuned Diffusion Importance Sampling (VT-DIS) adapts noise covariance to correct bias.
result VT-DIS achieves effective sample sizes of 80%, 35%, and 3.5% on benchmarks, using less computational budget.
New algorithm speeds up learning of graphical models.
problem Learning graphical models with sparse structure efficiently.
method Vertex-greedy score-based algorithm for learning DAGs.
result Polynomial runtime for learning DAG models.
New Wasserstein divergence improves generative model robustness and structure preservation.
problem Improving generative model robustness and structure preservation.
method Introduces a novel Wasserstein-1 path-space divergence and a WUP theorem.
result Derives robustness and generalization bounds for flow-based models.
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.
Improved score-based models generate high-quality images up to 256x256.
problem Training score-based models for high-resolution images is unstable and limited.
method Theoretical analysis, exponential moving average of model weights.
result Score-based models can generate high-fidelity images up to 256x256.
DualVDT improves time-series forecasting with a novel dual reparametrized structure.
problem Time-series forecasting with improved performance and analytical rigor.
method Dual reparametrized variational mechanisms on VAE, latent score based generative model, reverse time stochastic differential equation, variational ancestral sampling, KL divergence reduction.
result Advanced performance in time-series forecasting with reduced KL divergence.
New score-based methods identify causal structures with latent variables.
problem Identifying causal structures involving latent variables.
method Score-based methods with identifiability guarantees.
result Score equivalence and consistency for latent variable causal models.
Paper analyzes stability and forgetting in score-based generative models.
problem Understanding the stability and long-time behavior of generative models.
method Quantitative bounds on sampling error using stability and forgetting properties of the Markov chain.
result Provides practical consequences of stability and contraction mechanism in sampling.
CSDI improves time series imputation by 40-65% over existing methods.
problem Imputing missing values in time series data.
method Conditional Score-based Diffusion models conditioned on observed data.
result CSDI improves by 40-65% over existing probabilistic imputation methods on popular metrics.
RSGMs extend SGMs to Riemannian manifolds for better data modeling.
problem Current SGMs are limited to Euclidean spaces; RSGMs handle Riemannian manifolds.
method RSGMs use a noising stage with a diffusion process and a denoising model approximating the time-reversal of the diffusion on Riemannian manifolds.
result RSGMs improve generative modeling for data on Riemannian manifolds.
Wavelet SGM accelerates generative modeling with linear time complexity.
problem High computational cost in SGMs.
method Factorizing data distribution into wavelet coefficients.
result WSGM synthesizes wavelet coefficients with linear time complexity.
This research analyzes and accelerates score-based diffusion models using discretization and Hessian information.
problem Theoretical foundations and convergence analysis of score-based diffusion models.
method Investigation of various discretization schemes, including Euler, exponential integrators, and midpoint randomization. Proposal of an accelerated sampler based on local linearization method.
result Hessian-based approach achieves faster convergence rates of order $\widetilde{\mathcal{O}}\left(\frac{1}{\varepsilon}
ight)$, significantly improving upon vanilla diffusion models.
A new method for Bayesian inference using diffusion models.
problem Bayesian inference in simulator-based models.
method Score-based diffusion models trained with a sequential training procedure.
result Comparable or superior performance compared to existing methods.
New approach to score function in diffusion models using Malliavin calculus.
problem Estimating score function for complex data distributions.
method Combines Malliavin calculus with Bismut-type formula to derive exact score function expression.
result Derives exact, closed-form expression for score function in diffusion models.
MASF improves score-based filters for high-dimensional nonlinear systems with spatially sparse measurements.
problem Challenges in data assimilation for nonlinear, high-dimensional systems with spatially sparse measurements.
method Developed a forward process tailored for filtering that transforms the system state toward the measurement space, enabling a theoretically sound formulation of the likelihood score.
result MASF shows improved performance over existing score-based filters and ensemble-type Kalman filters, achieving up to a 28.2× wall-clock speedup.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
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.
New method for generating images with conditional probability models.
problem Generating images with specific conditions.
method Score-based diffusion models with theoretical analysis and new estimator.
result New estimator for conditional score performs similarly to state-of-the-art.
We introduce SADs to reveal how network architecture shapes score-based generative models.
problem Understanding and predicting the inductive biases of score-based generative models.
method Introducing Score Anisotropy Directions (SADs) to analyze network architecture.
result SADs reliably capture model behavior and correlate with performance.
Accelerates data generation in score-based models.
problem Slow generation of realistic data by score-based models.
method Developed an adaptive step size SDE solver.
result Generates data 2-10 times faster with high quality.
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.
Score-based generative models achieve state-of-the-art classification accuracy on CIFAR-10.
problem Improving classification accuracy on natural image datasets.
method Score-based generative models applied to CIFAR-10.
result Score-based models achieve state-of-the-art classification accuracy on CIFAR-10.
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.
New method synthesizes data on curved spaces for better interpolation.
problem Synthesizing data on curved spaces for better interpolation.
method Riemannian Diffusion Schrödinger Bridge
result Generalizes Diffusion Schrödinger Bridge to curved spaces for better interpolation.
A framework for sensitivity measures using scoring functions.
problem Constructing sensitivity measures for any elicitable functional.
method Score-based sensitivities constructed via consistent scoring functions.
result Demonstrated intuitive and desirable properties of score-based sensitivities.
New method for data assimilation using score-based models.
problem Bayesian inverse problem of identifying plausible state trajectories.
method Score-based data assimilation, learning a score-based generative model of state trajectories.
result Effective method for zero-shot observation scenarios.
CMCD sampler connects transport and variational inference for efficient sampling.
problem Efficient sampling and generative modeling in Bayesian computation.
method Developed a principled framework using divergences on path space, CMCD sampler with adaptive dynamics.
result CMCD sampler outperforms competing approaches across various experiments.
Unified approach unites GANs and diffusion models using particle methods.
problem Combining GANs and diffusion models for generative tasks.
method Proposes a unified framework where generator training is seen as a generalization of particle models.
result Demonstrates that GANs and diffusion models can be integrated within a unified framework.
SFG improves on-manifold sampling without labels or additional training.
problem Guiding score-based models on manifolds without labeled data or extra training.
method Developed saddle-free guidance (SFG) that uses curvature of log density estimates.
result SFG achieves state-of-the-art metrics in image generation without labeled data or additional training.