Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
This note clarifies connections between Föllmer process and DDPM sampler.
problem Understanding the relationship between Föllmer process and DDPM sampler.
method Direct discretization of the Föllmer process and DDPM sampler analysis.
result Discretized Föllmer processes provide optimal hyper-parameters for DDPM samplers.
Improved DDPMs achieve high log-likelihoods and sample quality with fewer passes.
problem Improving log-likelihoods of DDPMs while maintaining high sample quality.
method Modifying DDPMs with learning variances and using precision-recall metrics.
result DDPMs can achieve competitive log-likelihoods with fewer forward passes.
DDPMs can reproduce medical image context, showing interpolation between samples.
problem Understanding DDPMs' ability to learn spatial context in medical imaging.
method Used stochastic context models (SCMs) to produce training data and assess DDPMs' performance.
result DDPMs can generate contextually correct images, interpolating between samples.
New research shows DDPM can adapt to data's intrinsic low dimensionality efficiently.
problem Theoretical inefficiency of DDPM in high-dimensional data.
method Investigates how DDPM can exploit intrinsic low dimensionality of data.
result Proves DDPM's iteration complexity scales nearly linearly with intrinsic dimension k k k . The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.
problem Understanding and controlling errors in discrete-time DDPMs.
method Structural analysis of score functions, Schrödinger's problem, and FBSDEs.
result Explicit upper bound for total variation distance between sampling and target distributions.
PNDMs accelerate DDPMs by treating them as differential equations on manifolds.
problem Accelerate DDPMs while maintaining sample quality.
method Propose pseudo numerical methods (PNDMs) to solve differential equations on manifolds.
result PNDMs generate higher quality images with only 50 steps compared to 1000-step DDIMs (20x speedup).
This study shows how DDPM can be represented by the OU process.
problem Designing optimal noise schedules for DDPM.
method Formal equivalence between DDPM and OU process, heuristic designs based on Fisher Information.
result Fisher-Information-motivated schedule corresponds to cosine noise schedule.
Simplified explanation of DDPMs for machine learning.
problem Complexity in explaining DDPMs and missing rationale.
method Six simple steps to explain DDPMs.
result Clear rationale for each step of DDPM formulation.
Paper adapts DDPM to low-dimensional structures in image distributions.
problem Understanding and adapting to low-dimensional structures in image distributions.
method Developed a novel set of analysis tools to characterize algorithmic dynamics.
result First theoretical demonstration that DDPM can adapt to unknown low-dimensional structures.
WaveFit uses fixed-point iteration to create high-quality neural vocoders.
problem Creating high-quality neural vocoders with fast inference.
method Integrates GANs' adversarial training into a DDPM-like iterative framework based on fixed-point iteration.
result WaveFit synthesizes speech with naturalness comparable to human speech, and is significantly faster than existing methods.
DDPMs are robust to noisy score estimates and achieve optimal convergence rates in Wasserstein-2 distance.
problem Evaluating the quality of DDPMs in Wasserstein distance with noisy score estimates.
method Established finite-sample guarantees in Wasserstein-2 distance for DDPMs, considering noisy score estimates.
result Optimal convergence rates in Wasserstein-2 distance for DDPMs, matching Gaussian case.
SpecGrad improves neural vocoder sound quality by adapting diffusion noise to log-mel spectrogram.
problem Improving neural vocoder sound quality, especially in high-frequency bands.
method Adapting the diffusion noise distribution to the conditioning log-mel spectrogram through time-varying filtering.
result SpecGrad generates higher-fidelity speech waveform than conventional DDPM-based neural vocoders.
Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.
problem Sampling error bounds for DDPMs in 2-Wasserstein distance.
method Lipschitz-type conditions on score function, Föllmer process, and log-concave target distributions.
result Sharp upper bounds for DDPMs in 2-Wasserstein distance, optimal in dimension and steps.
DLPM replaces Gaussian noise with α-stable noise in DDPM, improving data distribution coverage and robustness.
problem Handling mode collapse and class imbalance in datasets with heavy-tailed noise.
method Extending DDPM to use α-stable noise, simplifying the process with elementary proof techniques.
result DLPM yields better coverage of data distribution tails, improved robustness to unbalanced datasets, and faster computation times.
Paper proposes SPD-DDPM for SPD matrices, improving on previous discriminative models.
problem Challenges in handling large-scale SPD matrix data for discriminative models.
method Introduces a generative model using Gaussian distribution in SPD space, allowing unconditional and conditional predictions.
result Effective fitting of data distribution and accurate predictions on both conditional and unconditional data.
Generative model uses DDPMs for risk-neutral derivative pricing.
problem Derivative pricing using arbitrage-free models.
method Developed a framework using DDPMs to generate risk-neutral asset price dynamics.
result Empirically validated the method for both European and path-dependent derivatives.
Diffusion models achieve high-quality samples from complex high-dimensional Gaussian mixtures without scaling with dimension.
problem Achieving accurate sampling from high-dimensional distributions using diffusion models.
method Investigates the effectiveness of diffusion models in sampling from Gaussian Mixture Models (GMMs) without scaling with dimension.
result DDPM requires at most O ( 1 / ε ) O(1/\varepsilon) O ( 1/ ε ) iterations to attain an ε \varepsilon ε -accurate distribution in total variation distance, independent of dimension and number of components. New method speeds up generative modeling without requiring diffusion steps.
problem Improving the speed and efficiency of generative modeling techniques.
method Probability flow ODE with a corrector step, achieving better dimension dependence.
result Better dimension dependence ( O ( d ) O(\sqrt{d}) O ( d ) vs. O ( d ) O(d) O ( d ) , assuming smoothness of the data distribution). A new model designs molecular latent vectors for drug discovery.
problem Designing effective molecular descriptors from molecular structures.
method Proposes a denoising diffusion probabilistic model (DDPM) for variational autoencoding molecular graphs.
result Demonstrates superior prediction performance and robustness compared to existing approaches.
The paper shows diffusion models can converge faster to a target distribution with low-dimensional structure.
problem Improving the convergence rate of diffusion models to target distributions.
method Analyzing DDIM and DDPM samplers under low-dimensional structure assumptions.
result The iteration complexities of DDIM and DDPM are no greater than k / ε k/\varepsilon k / ε in total variation distance. Proposes using diffusion models for probabilistic stock market predictions.
problem Uncertainties in financial data make deterministic models ineffective for stock market predictions.
method Utilizes Denoising Diffusion Probabilistic Models (DDPM) and Masked Relational Transformer (MRT).
result Achieves state-of-the-art performance in stock movement prediction and portfolio management.
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. Few-Shot Diffusion Models generate new samples from small image sets.
problem Generating new samples from a few images.
method Conditional Denoising Diffusion Probabilistic Models (DDPM) with patch-based input set information.
result FSDM can generate samples from previously unseen classes conditioned on as few as 5 samples.
DSPM models control noise volatility, improving financial data analysis.
problem Financial returns exhibit volatility clustering, challenging traditional models.
method DSPM uses a tempered-stable subordinator to control noise volatility, preserving kurtosis and autocorrelation.
result DSPM models accurately capture volatility clustering and noise mechanisms.
DARL uses DDPMs to generate synthetic market crash scenarios for robust portfolio optimization.
problem Challenges in capturing complex market dynamics and aligning with diverse investor preferences.
method Synergistic integration of DDPMs and DRL for portfolio management.
result DARL outperforms traditional methods in delivering superior risk-adjusted returns and resilience against crises.
DIN framework directly models hydraulic conductivity and uncertainty.
problem Modeling hydraulic conductivity and uncertainty in groundwater flow.
method DIN utilizes DDPM as a prior learner, incorporating observational data through conditional injection mechanisms.
result DIN generates multiple constraint-satisfying realizations and accurate uncertainty quantification.
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.
Gradient descent on DDPM objective learns Gaussian mixtures efficiently.
problem Learning Gaussian mixtures using gradient-based methods.
method Gradient descent on DDPM objective, connecting to EM and spectral methods.
result Gradient descent can efficiently recover Gaussian mixture parameters under certain conditions.
New Fourier-based diffusion model improves high-frequency generation quality.
problem Diffusion models struggle with high-frequency details.
method Analyzed and modified the forward process in Fourier space to equalize noise corruption across frequencies.
result Improved generation quality for high-frequency components.
Paper establishes fast convergence theory for diffusion models under minimal assumptions.
problem Establish theoretical guarantees for diffusion models under minimal assumptions.
method Developed a convergence theory for denoising diffusion probabilistic models (DDPM) under minimal assumptions.
result Achieved convergence rate of O(d/T) for target distributions with finite first-order moment.
A new DDPM for link prediction using sub-graph likelihood estimation.
problem Link prediction in graph domains.
method Sub-graph based diffusion model with DDPMs, decomposing likelihood estimation.
result Our model achieves superior performance in link prediction across various datasets.
GCDM generates valid large 3D molecules and optimizes existing molecules.
problem Lack of geometric properties in 3D molecule generation models.
method Introduces Geometry-Complete Diffusion Model (GCDM) using equivariant GNNs.
result Significantly outperforms existing models in 3D molecule generation and optimization.
Study shows diffusion models adapt to manifold hypothesis without dimensionality issues.
problem Empirical success of diffusion models in high-dimensional data.
method Developed a new framework connecting diffusion models to Gaussian Processes theory.
result Achieves rates independent of ambient dimension in terms of score learning and sampling complexity.
Study explores efficient continual learning of diffusion models.
problem Efficiently reusing computation in training diffusion models as data evolves.
method Benchmarked and analyzed CL methods for Denoising Diffusion Probabilistic Models (DDPMs).
result Experience replay with reduced rehearsal coefficient shows strong performance.
Unified normative modeling for neuroimaging phenotypes using denoising diffusion models.
problem Discarding multivariate dependence in neuroimaging pipelines.
method Denoising diffusion probabilistic models (DDPMs) with FiLM and SAINT backbones.
result Unified multivariate normative modeling with better calibration and dependence preservation.
Generates financial time series with stylized facts using diffusion models.
problem Generating realistic synthetic financial time series with statistical properties like fat tails, volatility clustering, and seasonality.
method Utilizes denoising diffusion probabilistic models (DDPMs) with wavelet transformation to convert and generate financial time series.
result Demonstrates that the proposed approach satisfies stylized financial time series properties.
Paper bridges score estimation to parameter and density estimation in DDPMs.
problem Efficiently estimating scores for generative models.
method Introduces a framework linking score estimation to parameter and density estimation.
result Denoising score-matching in DDPMs is asymptotically efficient for parameter estimation.
Paper introduces a new sampling method combining Consistency Models with importance sampling.
problem Inherent errors in samples and high NFEs for high-quality samples in Boltzmann distributions.
method Combines Consistency Models with importance sampling to produce unbiased samples with minimal NFEs.
result Produces unbiased samples using only 6-25 NFEs, comparable to 100 NFEs for DDPMs.
Replacing MSE with f-divergence in diffusion models improves robustness under data contamination.
problem Improving robustness of diffusion models under data contamination.
method Replacing MSE with f-divergence in diffusion models.
result Empirical improvement in performance under data contamination.
Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
IFH models graph generation with adjustable sequentiality.
problem Designing flexible graph generation models between one-shot and sequential approaches.
method Based on DDPM, IFH uses a node removal process to generate graphs with adjustable sequentiality.
result IFH models improve graph generation quality and efficiency compared to current methods.
HyFAD improves time series imputation by combining time and frequency diffusion.
problem Improve time series imputation by handling frequency-sensitive denoising and balancing global and local dynamics.
method HyFAD is a hybrid time-frequency diffusion model with frequency-aware embedding, built on DDPM paradigm.
result HyFAD achieves state-of-the-art performance in time series imputation.
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 model detects anomalies without needing clean data.
problem Anomaly detection without clean data.
method Robust denoising diffusion probabilistic models (RDDPM) using robust regression.
result Significantly outperforms existing methods in anomaly segmentation.
The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.
problem Developing a mathematical framework for denoising diffusion models in noncommutative settings.
method Formulating diffusion and reverse processes governed by operator-valued stochastic dynamics, using tools from free stochastic analysis.
result Establishing an information-geometric link between entropy production, transport, and deconvolution.
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.
New theory improves diffusion models' convergence rates.
problem Understanding and optimizing diffusion models for faster data generation.
method Developed non-asymptotic theory for diffusion models with minimal assumptions.
result Established convergence rates for two diffusion models.