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.
A new diffusion model improves time-series forecasting by preserving seasonal patterns.
problem Improving time-series forecasting accuracy, especially for seasonal data.
method A forward diffusion process that decomposes signals into spectral components, altering only the diffusion process.
result The method maintains high signal-to-noise ratios for dominant frequencies, improving long-term pattern recovery.
Optimal wealth strategy derived for jump-diffusion models with liabilities.
problem Maximizing utility in jump-diffusion models with random liabilities.
method Forward Backward SDEs system for optimal strategy.
result Explicit results for pure jump model and exponential utilities.
FLDD improves discrete diffusion models by learning a non-Markovian noising process.
problem Efficiency and quality of discrete diffusion models in few-step generation.
method Introduces a learnable non-Markovian forward (noising) process to match the target distribution.
result FLDD produces higher quality samples in fewer steps compared to conventional discrete diffusion models.
Diffusion-GAN uses diffusion to improve GAN training stability and realism.
problem Stability and realism issues in training GANs.
method Diffusion-GAN employs a forward diffusion chain to generate Gaussian-mixture distributed instance noise, with adaptive diffusion process and timestep-dependent discriminator.
result Diffusion-GAN produces more realistic images with higher stability and data efficiency.
EnKG solves inverse problems without derivatives, using diffusion models.
problem Solving inverse problems with derivative-free methods.
method Ensemble Kalman Diffusion Guidance (EnKG) using diffusion models.
result EnKG can solve inverse problems with only forward model evaluations.
Improved language generation with faster sampling speed.
problem Speed and coherence issues in autoregressive language models.
method Introduces Neural Flow Diffusion Models (NFDM) for discrete state spaces.
result Substantially reduces likelihood gap with autoregressive models.
The paper analyzes performance criteria for competing fund managers in Ito-diffusion markets.
problem Analyzing performance of competing fund managers in Ito-diffusion markets.
method Developed forward relative performance criteria and forward Nash equilibrium for passive and competitive cases.
result Extended performance criteria for investment problems in Ito-diffusion markets.
New method solves blind inverse problems by optimizing both operator and image parameters.
problem Solving blind inverse problems with known forward operator.
method Parallel reverse diffusion guided by gradients from intermediate stages.
result State-of-the-art performance on blind deblurring and imaging through turbulence.
Blade uses diffusion priors to accurately and calibratedly infer complex systems.
problem Derivative-free Bayesian inversion for high-dimensional, nonlinear problems with costly forward models.
method Blade employs an ensemble of interacting particles and diffusion models as priors, querying forward models only through evaluations.
result Blade produces well-calibrated posterior samples that existing methods cannot, improving with more iterations and particles.
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.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
A new first-order sampler improves diffusion probabilistic model sampling quality.
problem The belief that first-order methods are inherently slower for diffusion probabilistic model sampling.
method A novel training-free, first-order sampler that approximates the forward-value evaluation via a one-step lookahead predictor.
result The proposed sampler provably approximates the ideal forward-value trajectory while retaining first-order convergence and can improve sample quality under the same NFE budget.
Faster diffusion-based models generate data with fewer steps.
problem Slow and costly diffusion-based generative models.
method Truncate diffusion process to generate data more efficiently.
result Truncated models provide consistent improvements in performance.
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.
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.
New method for efficient conditional sampling from diffusion models.
problem Efficient conditional simulation from diffusion models.
method Explicit forward-backward bridging to express conditional simulation as an inference problem.
result Principled particle Gibbs and pseudo-marginal samplers for conditional distribution.
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.
CCDF reduces diffusion sampling steps for inverse problems.
problem Slow sampling from diffusion models in inverse problems.
method Starting from a single forward diffusion step with better initialization, followed by stochastic contraction.
result Significantly reduced sampling steps for state-of-the-art reconstruction.
Introduces VSMD to improve generative diffusion processes without high costs.
problem High training costs and scalability issues in generative diffusion processes.
method Introduces variational Schrödinger momentum diffusion (VSMD) with adaptively transport-optimized variational scores and critical-damping transform.
result Efficiently generates anisotropic shapes while maintaining transport efficacy, outperforming alternatives.
New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.
problem Numerical stability issues in diffusion sampling despite small forward-marginal error.
method Constructing a smooth score field with arbitrarily small forward-marginal L2 error, showing nonexplosive behavior and moments of every order. result Euler--Maruyama discretizations can converge in probability even when moments diverge, demonstrating failure of weak convergence.
The paper tackles singularities in diffusion models on submanifolds.
problem Analyzing singularities in diffusion models on lower-dimensional submanifolds.
method Small-time approximations of the Green's function and derivation of a new target function.
result The new target function remains bounded for singular data 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 for multi-modal data distributions. This work extends diffusion models to function space for better generative modeling.
problem Limited applicability of diffusion models to functional data domains.
method Introduces Denoising Diffusion Operators (DDOs) for training diffusion models in function space.
result Demonstrates accurate function-valued generation at fixed cost.
New method improves quality and efficiency of generative models by using smaller diffusion times.
problem Lack of theoretical understanding of diffusion time T in score-based diffusion models.
method Introduce an auxiliary model to bridge the gap between ideal and simulated dynamics, followed by reverse diffusion.
result Empirical results show competitive performance in image data compared to state-of-the-art models.
Diffusion models reveal latent hierarchical structure in data.
problem Quantitative measurement of data's hierarchical structure.
method Forward-backward experiments in diffusion models.
result Changes in latent variables manifest as correlated chunks in data.
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.
Paper establishes a density formula for diffusion models, linking target density to score function.
problem Lack of theoretical foundation for optimizing DDPMs using ELBO.
method Developed a density formula for continuous-time diffusion processes, revealing the connection between target density and score function.
result The minimizer of the ELBO objective for DDPMs nearly coincides with the true objective, providing a theoretical foundation.
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.
New method reduces diffusion model function evaluations for discrete data.
problem High computational burden in generating samples from masked diffusion models.
method Modified causal attention mask and speculative sampling mechanism for non-factorized predictions.
result Achieved ~2x reduction in required network forward passes.
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.
This primer explains diffusion models in general state spaces.
problem Diffusion models in general state spaces are not well-introduced.
method Develops discrete-time and continuous-time views of diffusion models, deriving Fokker-Planck and master equations.
result Unified understanding of diffusion models across continuous and discrete domains.
New sampling method uses stochastic interpolants and FBSDEs.
problem Sampling from high-dimensional distributions with unnormalized densities.
method Stochastic interpolants and FBSDEs to define and solve diffusion process.
result Effective sampling from challenging distributions.
RML improves generative modeling of complex distributions.
problem Learning complex distributions in applications.
method RML defines a forward process to a known distribution, then learns a reverse Markov process.
result RML efficiently captures complex distributions in simulations and climate data.
In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strik…
CPS solves inverse problems using forward passes and constrained particle seeking.
problem Solving inverse problems with limited forward observation information.
method Gradient-free approach that reformulates inverse problem as constrained optimization.
result CPS achieves results comparable to gradient-based methods while outperforming alternatives.
New bidirectional model predicts magnetohydrodynamics fields and estimates uncertainty.
problem Predicting multiple fields in magnetohydrodynamics with uncertainty.
method Bidirectional autoregressive latent diffusion approach.
result Model can estimate uncertainty without ground truth using self-supervised consistency.
Develops a robust method for image reconstruction from limited data.
problem Inference of unknown images from few measurements, often ill-posed.
method Introduces DPnP, a diffusion plug-and-play method combining likelihood and score-based samplers.
result Establishes performance guarantees for DPnP, demonstrating robustness and efficiency.
Model-free expression for SSR derived in terms of characteristic function.
problem Calculating the skew-stickiness-ratio (SSR) in financial markets.
method Model-free expression using characteristic function, focusing on diffusion and affine forward variance cases.
result General formula for SSR simplifies and becomes particularly tractable in affine forward variance cases, with a limit of H+3/2 for short-term limit. Unified analysis for deterministic samplers in diffusion models.
problem Challenges in analyzing deterministic samplers for diffusion models.
method Unified convergence analysis framework.
result Achieved polynomial iteration complexity for DDIM-type samplers.
QTD integrates quantization with diffusion for efficient data generation.
problem Challenges in continuous diffusion models, especially long-range transitions and biases.
method Quantized Transition Diffusion (QTD) integrates data quantization with discrete diffusion dynamics.
result QTD achieves efficient data generation with minimal score evaluations.
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.
Study numerical methods for singular FBSDEs with degenerate forward component.
problem Numerical approximation of singular fully coupled FBSDEs with degenerate forward component and non-smooth terminal condition.
method Splitting approach to treat diffusion and transport parts separately.
result The splitting method converges with rate 1/2 under structural condition.
DSB approximates SB problem for faster generative modeling.
problem Fast generation from complex data distributions.
method Entropy-regularized optimal transport on path spaces.
result DSB yields faster convergence to data distribution.
Iterative tilting fine-tunes diffusion models for reward-tilted distributions.
problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.
Neural network approximates diffusion bridges for efficiency and robustness.
problem Efficient simulation of conditioned diffusion processes, especially rare events and multimodal distributions.
method Trains a neural network to approximate bridge dynamics, eliminating MCMC and score modeling.
result Efficient sampling of conditioned diffusion bridges at comparable cost to unconditioned process.
Framework uses diffusion models to infer material properties from noisy mechanical measurements.
problem Inference of spatially varying material properties from noisy mechanical responses.
method Conditional score-based diffusion models approximating the score function of a conditional distribution.
result Framework can efficiently solve large-scale physics-based inverse problems.
A new method for diffusion generative models improves sample quality and speed.
problem Improving the efficiency and quality of diffusion generative models.
method Developed a complete recipe for forward diffusion processes in SGMs, introducing PSLD.
result PSLD achieves superior sample quality and speed compared to existing methods.