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-leaping scheme in KL divergence. A new method for decision-focused learning using diffusion models.
problem Inability of deterministic point predictions to capture stochasticity in real-world environments.
method Proposes a diffusion-based DFL approach that trains a diffusion model to represent uncertain parameters and optimizes decisions through stochastic optimization.
result Empirically shows consistent outperformance over strong baselines in decision quality.
A new method speeds up sampling in diffusion models.
problem Slow sample generation in diffusion models.
method Proposed Splitting Integrators for fast stochastic sampling.
result Achieved FID score of 2.36 in 100 NFE, significantly faster than baselines.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we …
Develops polynomial diffusion models for multi-factor commodity futures dynamics.
problem Modeling futures prices using latent state variables for short and long-term stochastic factors.
method Polynomial diffusion models to incorporate non-linear effects, two filtering methods for estimation.
result Accurate estimation of futures prices despite parameter identification issues in polynomial diffusion models.
SA-Solver improves stochastic sampling from DPMs.
problem Efficient sampling from Diffusion Probabilistic Models (DPMs) is time-consuming.
method Proposes SA-Solver, an improved stochastic Adams method for solving diffusion SDE.
result SA-Solver achieves improved or comparable performance compared to SOTA methods for few-step sampling.
Paper proposes a new method to speed up diffusion models.
problem High computational cost of sampling from diffusion models.
method Stochastic Runge-Kutta method for acceleration.
result Provable acceleration with reduced score function evaluations.
Bayesian inference for stochastic differential equations using Wishart diffusions.
problem Inferring stochastic differential equations for regression and dynamical modeling.
method Bayesian non-parametric approach with semi-parametric Wishart processes.
result Modeling diffusion in stochastic differential equations improves performance and avoids overfitting.
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.
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.
Estimates drift functions in SDEs using denoising diffusion models.
problem Estimating time-homogeneous drift functions in multivariate SDEs.
method Formulates drift estimation as a denoising problem, trains a conditional diffusion model.
result Proposed estimator matches classical methods in low dimensions and remains competitive in higher dimensions.
This paper extends neural network approximation results to denoising diffusion models.
problem Improving the efficiency and accuracy of generative models.
method Leveraging connections to stochastic control and neural network approximation.
result Established neural network approximation results for the Föllmer drift are extended to denoising diffusion models.
Diffusion models' speed-accuracy relations derived from thermodynamics.
problem Understanding the trade-off between model speed and accuracy.
method Connecting diffusion models to thermodynamics and optimal transport.
result Speed-accuracy relations derived, providing insights into optimal learning protocols.
New sampling and diffusion models methods introduced without density function assumptions.
problem Sampling and diffusion models without regularity assumptions.
method Inspired by reverse diffusion process, novel sampling and diffusion algorithms.
result Explicit convergence rate and dimension-free particle approximation convergence result.
This work formalizes guidance in diffusion models and introduces a stochastic control framework.
problem Lack of a solid theoretical foundation for guidance scheduling in diffusion models.
method Introduces a stochastic optimal control framework to cast guidance scheduling as an adaptive optimization problem.
result Establishes a principled foundation for more effective guidance in diffusion models.
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate…
New method converts and optimizes sampling schedules for generative models.
problem Optimizing sampling schedules for generative models like flows and diffusions.
method Unified framework for stochastic interpolants, including point mass schedules.
result Demonstrated efficient generation of images with fewer steps.
ProGen improves spatiotemporal forecasting with SDEs and diffusion models.
problem Complex spatial and temporal dependencies in spatiotemporal data.
method ProGen uses Stochastic Differential Equations and diffusion-based generative models.
result ProGen outperforms state-of-the-art models on traffic datasets.
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.
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
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.
Demon aligns diffusion models without retraining or backpropagation.
problem Aligning diffusion models with user preferences.
method Stochastic optimization to control noise distribution.
result Significantly improves aesthetics scores for text-to-image generation.
SymDiff uses stochastic symmetrisation for equivariant diffusion models.
problem Constructing equivariant diffusion models for data augmentation.
method Stochastic symmetrisation for lightweight, efficient, and easy-to-implement equivariance.
result SymDiff achieves significant empirical benefit for E(3)-equivariant molecular generation. 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.
Optimal control theory connects diffusion models to generative modeling.
problem Sampling from unnormalized densities in statistics and computational sciences.
method Deriving a Hamilton-Jacobi-Bellman equation and applying control theory to minimize Kullback-Leibler divergence.
result Time-reversed diffusion sampler (DIS) outperforms other diffusion-based sampling methods.
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.
Diffusion models mimic human actions in sequential tasks.
problem Cloning human behavior in dynamic environments is challenging.
method Adapting diffusion models to handle stochastic, multimodal, and correlated actions.
result Diffusion models closely replicate human behavior in robotic and gaming tasks.
Reflected Diffusion Models improve on score-based models by incorporating data constraints.
problem Numerical error in score-based models leads to unnatural samples.
method Reverses a reflected stochastic differential equation on data support, learning perturbed score function through generalized score matching loss.
result Improves sample quality and fidelity without architectural modifications.
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.
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.
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.
AugMask trains diffusion models on incomplete tabular data by augmenting missing values and applying denoising supervision.
problem Training diffusion models on incomplete tabular data with missing values.
method AugMask uses stochastic augmentation and denoising supervision to adapt diffusion models to incomplete data.
result AugMask enables diffusion-based tabular generators to outperform specialized missing-aware baselines across various datasets and missingness regimes.
Study on policy gradient for stochastic bandits using diffusion approximation.
problem Improving policy gradient methods for stochastic bandits with optimal regret bounds.
method Continuous-time diffusion approximation of policy gradient with learning rate analysis.
result Proved optimal regret bound of O(klog(k)log(n)/η) for η=O(Δ2/log(n)). Error estimates found between SGD with momentum and Langevin diffusion.
problem Quantifying the difference between SGD with momentum and Langevin diffusion.
method Established error estimates using 1-Wasserstein and total variation distances.
result Quantitative error estimates between SGD with momentum and underdamped Langevin diffusion.
In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions (X1,...,Xd), at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace th…
This work combines recurrent models with diffusion for probabilistic time series forecasting.
problem Scalability and capturing high-dimensional distributions and cross-feature dependencies in time series forecasting.
method Combines recurrent neural networks' efficiency with diffusion models' probabilistic modeling, using stochastic interpolants and conditional generation.
result Offers scalable probabilistic time series forecasting methods.
Efficient methods accelerate diffusion model sampling.
problem Slow sample generation in diffusion models.
method Conjugate Integrators and Splitting Integrators.
result Hybrid method achieves best FID scores.
This paper uses Malliavin calculus to price and compute delta of financial derivatives in jump-diffusion models.
problem Pricing and delta computation of financial derivatives in jump-diffusion models with stochastic intensity.
method Utilizes Malliavin calculus to price and compute delta, applying the Euler scheme for convergence analysis.
result Established the convergence of approximated solution, financial derivative, and its delta Greeks.
The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.
problem Large deviation principles for stochastic volatility models with reflection.
method Sample path and small-noise large deviation principles for the log-price process.
result Asymptotic behavior of binary barrier options and call prices in the small-noise regime.
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.
A stochastic model helps maintain insufficiently funded pension funds.
problem Maintaining pension funds that are underfunded and require external financing.
method A time-homogeneous diffusion process with a barrier is used to model the unrestricted reserves value, and a renewal-reward process models the financing effort.
result Expected values and cost evaluations of maintenance are derived, and the approach is applied to a generalized Brownian motion process.
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.
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
Diffusion-VAE tackles multi-step stock price prediction with stochastic noise.
problem Challenges in multi-step stock price prediction due to stochasticity and target price sequence.
method Combines hierarchical VAE and diffusion probabilistic techniques for seq2seq stock prediction.
result D-Va model outperforms state-of-the-art solutions in prediction accuracy and variance.
Adaptive learning of SPDE solutions using score-based diffusion models.
problem Model errors and reduced accuracy in SPDE solutions due to incomplete physical knowledge and environmental variability.
method Score-based diffusion models with recursive Bayesian inference, incorporating simulation data and observational information.
result Accuracy and robustness of the proposed method demonstrated on benchmark SPDEs.
The paper develops a new model for order book dynamics using Hawkes processes.
problem Capturing the dynamics of order flow and liquidity migration in financial markets.
method Develops a mesoscopic model using Hawkes processes to describe interactions between order arrivals, cancellations, and liquidity movement.
result Derives a diffusive limit for the order book dynamics, providing a unified framework for market microstructure.