Improved neural model for social recommendation by integrating social and interest networks.
problem Data sparsity and lack of higher-order relationships in social recommendation.
method DiffNet++ models neural influence diffusion and interest diffusion in a unified framework using a multi-level attention network.
result Extensive experiments on real-world datasets show the effectiveness of DiffNet++.
Study no-arbitrage conditions in 1D diffusion markets with interest rates.
problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.
The paper develops a new formula for financial pricing under multiple interest rates and collateralization.
problem Financial pricing under multiple interest rates and collateralization.
method Derives a change of measure formula for recursive conditional expectations in a jump-diffusion setting.
result Generalizes the change of numéraire technique for multiple interest rates and collateralization.
Develops a new method for pricing GMWBs with jumps and stochastic interest rates.
problem Pricing guaranteed minimum withdrawal benefits (GMWBs) with jumps and stochastic interest rates.
method Combines semi-Lagrangian method with Fourier pricing and Green's function.
result Mathematically demonstrates convergence to the viscosity solution of the HJB-QVI.
This work benchmarks diffusion model-based samplers for Bayesian inverse problems.
problem Optimizing diffusion models for uncertainty quantification in Bayesian inverse problems.
method Introduces three benchmark problems and a unified framework for diffusion model-based posterior sampling.
result Provides insights into strengths and limitations of diffusion model-based samplers.
Framework for training-free guidance in discrete diffusion models for molecular generation.
problem No equivalent training-free guidance methods for discrete diffusion models.
method Framework using guidance functions for discrete data.
result Demonstrated utility on molecular graph generation tasks.
Formula for European option pricing under jump diffusion model.
problem Option pricing under complex stochastic processes.
method Infinite series of Black-Scholes terms for Levy-driven processes.
result Series solution converges with a radius of convergence.
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.
FastVoiceGrad speeds up VC to one step, matching or surpassing quality.
problem Slow inference in multi-step diffusion-based VC.
method Adversarial Conditional Diffusion Distillation (ACDD) for one-step diffusion.
result One-shot VC with superior or comparable performance to multi-step methods.
Diffusion models learn balanced data representations, unlike classification models.
problem Understanding feature learning in diffusion models.
method Proposed a feature learning framework to analyze diffusion models' training dynamics.
result Diffusion models encourage learning balanced and comprehensive representations.
We approximate sticky diffusions using Markov chains for efficient simulation.
problem Approximating sticky diffusions for accurate simulation.
method CTMC approximation of sticky diffusions, efficient matrix exponentials, and Euler scheme comparison.
result Second order convergence of CTMC approximation for sticky diffusions.
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should ensure that the correlation coefficients are updated subject to the positive definite…
Study increasing profits in a flexible financial market model.
problem Characterize increasing profits in a 1D diffusion market with interest rates.
method Characterize increasing profits using an auxiliary deterministic signed measure and a canonical trading strategy.
result Existence and characterization of increasing profits in terms of ν and θ. Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features …
DPS uses PINNs to estimate drift in diffusion models for sampling.
problem Accurately estimating drift term in reverse SDE from unnormalized density.
method Diffusion-PINN Sampler (DPS) solves PINN for log-density of SDE marginals.
result DPS achieves convergence guarantees and accurately samples complex distributions.
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.
New method simulates diffusion bridges using score matching.
problem Simulating diffusion bridges for statistical inference.
method Backward time representation, variational formulation, score matching.
result Effective approximation of diffusion bridges.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.
problem Analyzing financial markets with sticky asset prices and proving no arbitrage conditions.
method Introduced a financial market model with a risky asset following a sticky geometric Brownian motion and a riskless asset with a constant interest rate. Proved no arbitrage conditions and derived pricing equations.
result No arbitrage conditions are met only when the interest rate is zero, and all replicable payoffs are derived under this condition.
First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback. But the Tsallis model is only one of a very large class of linear diffusion with…
Paper proposes a method to monitor research topic evolution.
problem Difficulty in tracking research topic diffusion and evolution.
method Deep Non-negative Autoencoder with information divergence measurement.
result Identifies evolution of research topics and discovers topic diffusions.
In the present paper, given an evolving mixture of probability densities, we define a candidate diffusion process whose marginal law follows the same evolution. We derive as a particular case a stochastic differential equation (SDE) admitting a unique strong solution and whose density evolves as a mixture of Gaussian d…
Study validates metrics for offline MBO using diffusion models.
problem Evaluate metrics for offline MBO without ground truth oracle.
method Propose and quantify validation metrics over datasets.
result Identify most effective validation metrics.
Diffusion models help in learning priors for Thompson Sampling in bandit problems.
problem Learning effective strategies for diverse bandit tasks.
method Training a denoising diffusion model to learn task distributions, combining with Thompson Sampling.
result The approach significantly improves performance across different bandit tasks.
We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a uniform set of assumptions on the log-posterior distribution, assuming it to be smo…
The paper models SOFR and EFFR dynamics, reconciling diffusive and piecewise paths.
problem Updating interest rate models for SOFR, which is becoming a key benchmark.
method Calibrates a model to SOFR and EFFR futures prices, reconciling diffusive and piecewise paths.
result The model reflects key empirical features of SOFR dynamics and reconciles diffusive and piecewise paths.
We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or sup…
We introduce the concept of Hypoelliptic Diffusion Maps (HDM), a framework generalizing Diffusion Maps in the context of manifold learning and dimensionality reduction. Standard non-linear dimensionality reduction methods (e.g., LLE, ISOMAP, Laplacian Eigenmaps, Diffusion Maps) focus on mining massive data sets using w…
EM Distillation simplifies diffusion models to one-step generators.
problem Efficient sampling from complex diffusion models with minimal loss of quality.
method EM Distillation, a maximum likelihood approach based on Expectation-Maximization.
result EM Distillation outperforms existing one-step generative methods in FID scores.
We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale …
Bernstein processes are Brownian diffusions that appear in Euclidean Quantum Mechanics. Knowledge of the symmetries of the Hamilton-Jacobi-Bellman equation associated with these processes allows one to obtain relations between stochastic processes (Lescot-Zambrini, Progress in Probability, vols 58 and 59). More recentl…
In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional Itô-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently regular density. In this article…
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged inst…
This paper uses diffusion models for lossy image compression, improving perceptual metrics and practicality.
problem Lossy image compression with improved perceptual metrics and practicality.
method End-to-end optimized lossy image compression using conditional diffusion models.
result The model yields stronger FID scores and competitive performance in distortion metrics.
The paper analyzes how guidance affects diffusion models using Gaussian mixture models.
problem Understanding how guidance influences diffusion models in specific contexts.
method Theoretical study using Gaussian mixture models and comparison inequalities for differential equations.
result Guidance boosts classification confidence but reduces distribution diversity, leading to lower differential entropy.
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
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.
We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator. Given the set of call and pu…
The paper analyzes diffusion condensation for data geometry and topology.
problem Understanding the geometry and topology of high-dimensional data.
method Time-inhomogeneous diffusion process with geometric, spectral, and topological analysis.
result The condensation process defines intrinsic condensation homology and ambient persistent homology.
This tutorial reviews RL-based methods for optimizing diffusion models to maximize specific metrics.
problem Optimizing diffusion models to generate samples that maximize specific metrics in practical applications.
method Various RL algorithms including PPO, differentiable optimization, reward-weighted MLE, value-weighted sampling, and path consistency learning.
result Exploration of strengths and limitations of RL-based fine-tuning algorithms and their benefits compared to non-RL-based approaches.
Tract-specific diffusion measures, as derived from brain diffusion MRI, have been linked to white matter tract structural integrity and neurodegeneration. As a consequence, there is a large interest in the automatic segmentation of white matter tract in diffusion tensor MRI data. Methods based on the tractography are p…
A novel framework refines diffusion models iteratively for better downstream reward optimization.
problem Optimizing reward functions during inference of diffusion models.
method Iterative refinement process with noising and reward-guided denoising steps.
result Superior empirical performance in protein and DNA design.
A new method approximates the exact posterior score for diffusion models.
problem Training-free guidance of diffusion models for image restoration and inverse problems.
method Presented a novel expression for the exact posterior score, leveraging it to compute step sizes on the fly.
result Demonstrated competitive performance with fewer time steps compared to state-of-the-art techniques.
Extends diffusion models to non-Euclidean spaces with geometric priors.
problem Difficulties in natural sciences with symmetries and non-Euclidean data.
method Constructs a noising process and neural network equivariant to symmetry group, approximates score function.
result Model can generate complex scalar and vector fields on synthetic and real-world data.
A fast method approximates likelihood scores for noisy linear inverse problems.
problem Solving noisy linear inverse problems efficiently.
method Proposes a simple closed-form approximation to the likelihood score for diffusion and flow-based models.
result Significantly faster than baseline methods while maintaining competitive or better reconstruction performances.
Proposes a new model for estimating individual treatment effects.
problem Estimating individual treatment effects from observational data is challenging.
method Integrates diffusion modeling and conformal inference with propensity score and covariate approximation.
result Establishes rigorous theoretical guarantees and demonstrates competitive performance.
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to model two-alternative forced choice decisions, and, while simple formulae for ac…