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.
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 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.
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 …
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.
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.
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.
The paper develops stochastic methods on geometric spaces for transformations.
problem Existence and uniqueness of stochastic processes on geometric spaces.
method Stochastic parallel transport and equivariant diffusions on the group of diffeomorphisms.
result Existence and uniqueness of stochastic parallel transport and equivariant diffusions.
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.
Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential equations into the theoretical framework of diffusion approximation, extending the …
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.
Riemannian stochastic gradient descent approximates a diffusion process called Riemannian stochastic modified flow.
problem Improving convergence rate of Riemannian stochastic gradient descent.
method Using stochastic differential geometry, the paper shows RSGD can be approximated by the Riemannian stochastic modified flow (RSMF).
result RSGD can be approximated by the solution to the RSMF driven by an infinite-dimensional Wiener process, increasing the order of approximation.
The paper examines conditions for stochastic invariance of cones in SPDEs with jumps.
problem Stochastic invariance of cones in SPDEs with jumps.
method Sufficient conditions for stochastic invariance of closed convex cones in abstract L2-spaces. result Conditions for stochastic invariance of cones are provided and analyzed.
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.
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.
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.
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…
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.
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 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.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
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.
Uniform diffusion approximation for SGD in non-convex settings.
problem Finite-time diffusion approximation for SGD.
method Establishing uniform-in-time diffusion approximation with strong convexity and mild conditions.
result Uniform-in-time diffusion approximation of SGD without convexity of each loss function.
Novel framework for learning infinitesimal generator of stochastic processes.
problem Challenges in learning infinitesimal generator due to unbounded nature and state space dimensionality.
method Introduces a novel framework based on energy functional, integrates physical priors, and uses reduced-rank estimator in RKHS.
result Learning bounds independent of state space dimension and non-spurious spectral estimation.
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 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.
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.
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
Algorithm minimizes risk for multiclass classification of stochastic diffusion paths.
problem Multiclass classification of stochastic diffusion paths with distinct drift functions.
method Empirical risk minimization using L2 risk.
result Achieves fast rates of convergence under margin assumption.
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.
The paper develops a method for stochastic differential equations on manifolds using Schwartz morphisms and diffusion generators.
problem Representing stochastic differential equations on smooth manifolds.
method Using Schwartz morphisms and diffusion generators to construct SDEs on manifolds.
result An extended Ito formula for SDEs on manifolds.
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.
New method learns diffusion bridges for rare events.
problem Simulating rare events in diffusion processes.
method Iterative online learning based on self-consistency.
result Strong performance in various empirical settings.
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.
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. 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.
SGLDiff approximates Bayesian posterior distributions with subsampling error.
problem Approximating Bayesian posterior distributions in large-scale data settings.
method Stochastic Gradient Langevin Diffusion (SGLDiff) with subsampling.
result The Wasserstein distance between the posterior and SGLDiff's limiting distribution is bounded by a fractional power of the mean waiting time.
New method distinguishes stochastic from deterministic signals using excursion counts.
problem Distinguishing between stochastic and deterministic signals in discrete time series.
method Excursion and crossing theorems for continuous semimartingales, comparing empirical excursion counts to theoretical expectation.
result A robust data-driven diffusion test that classifies signals based on log-log slope deviation.
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.
Incomplete financial markets are considered, defined by a multi-dimensional non-homogeneous diffusion process, being the direct sum of an Itô process (the price process), and another non-homogeneous diffusion process (the exogenous process, representing exogenous stochastic sources). The drift and the diffusion matrix …
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…
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…