Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.
problem Constructing multi-view diffusion geometries with flexible view interaction and fusion.
method Intertwined multi-view diffusion trajectories (MDTs) as a class of inhomogeneous diffusion processes.
result Established theoretical properties and derived diffusion distances and embeddings.
Physics-informed diffusion model detects anomalous trajectories in GPS data.
problem Detecting fake GPS trajectories in international waters.
method Physics-informed diffusion model integrating kinematic constraints.
result Higher prediction accuracy and lower error rate for anomaly detection.
TGD improves conditional sampling by concentrating computation on promising trajectories.
problem Efficiently training-free conditional sampling with diffusion priors.
method Tempered Guided Diffusion (TGD) using annealed sequential Monte Carlo.
result TGD yields a consistent particle approximation to the posterior as the number of particles grows.
ELM combines machine learning and feature engineering for anomalous diffusion detection.
problem Quantitative characterization of anomalous diffusion from single trajectories.
method Extreme Learning Machine (ELM) combined with feature engineering.
result ELM achieves satisfactory performance in AnDi challenge tasks.
CoTj improves diffusion model quality and stability via graph planning.
problem Rigidity in diffusion models due to high-dimensional state space.
method Chain-of-Trajectories (CoTj) framework using Diffusion DNA for graph planning.
result CoTj discovers context-aware trajectories improving output quality and stability.
Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.
problem Understanding the geometric structure of diffusion-based generative models.
method Characterization of deterministic sampling trajectories using low-dimensional subspace and kernel-estimated data modeling.
result Sampling trajectories in diffusion models are confined to a low-dimensional subspace and exhibit a boomerang shape.
New method guides pretrained diffusion models without additional training.
problem Guidance methods for diffusion models often require extra training or are task-specific.
method Variational Control using Diffusion Trajectory Matching (DTM)
result Achieves state-of-the-art results on various problems.
DGFS improves sampling from complex densities by optimizing partial trajectories.
problem Sampling from intractable high-dimensional density functions.
method DGFS uses a flow function to break down the training process into short partial trajectory segments, leveraging intermediate learning signals.
result DGFS achieves more accurate estimates of the normalization constant.
The paper examines the sampling dynamics of diffusion models using ODEs.
problem Understanding the sampling dynamics of diffusion models.
method Careful inspection of ODE-based sampling of SDEs, revealing structures and relationships.
result Established a theoretical relationship between optimal ODE-based sampling and mean-shift algorithm.
CTM improves diffusion model sampling quality with efficient ODE traversal.
problem Lack of natural trade-off between sample quality and speed in consistency models.
method CTM trains a neural network to output scores and traverse ODE trajectories efficiently.
result CTM achieves state-of-the-art FIDs and improves sample quality with increased computational budget.
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.
Stochastic gradient descent's long-term fluctuations are described by a diffusion limit.
problem Long-term behavior of stochastic gradient descent in non-smooth settings.
method Functional central limit theorem applied to rescaled trajectory of SGD.
result Characterization of long-term fluctuations around the minimizer.
Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this…
The paper develops a neural network-based classifier for diffusion process drifts.
problem Classifying diffusion processes with distinct drift functions from discrete observations.
method Derives a Bayes rule and constructs a plug-in classifier using neural networks to estimate drifts.
result Establishes convergence rates for misclassification risk, highlighting benefits of diffusion structure.
This work extends ME-RL using diffusion models to sample optimal policies.
problem Sampling from the optimal policy trajectory distribution in ME-RL.
method Introducing Diffusion-Augmented Markov Decision Processes (DA-MDPs) to minimize reverse KL divergence.
result DA-MDPs enable seamless integration into various ME-RL methods and outperform baselines.
Paper presents a probabilistic framework for diffusion synchronization.
problem Improper application of heuristics leads to suboptimal results in diffusion synchronization.
method Develops a probabilistic framework to analyze and adapt correlation models for each specific task.
result Achieves better results by identifying optimal correlation models per task.
Unified framework improves diffusion model rewards without full trajectories.
problem Limited theoretical understanding of guided diffusion samplers.
method Developed a unified algorithmic and theoretical framework for diffusion guidance and reward-guided diffusion.
result Framework shows CFG decreases expected reciprocal of classifier probability.
Develops a new model for controllable and realistic traffic simulation.
problem Lack of models that offer both controllability and realism in traffic simulation.
method Guided Conditional Diffusion (CTG) model using diffusion modeling and differentiable logic.
result Improves controllability-realism tradeoff over strong baselines.
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.
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.
Diffusion models simulate molecular dynamics with adjustable accuracy.
problem Simulating molecular dynamics with high accuracy and efficiency.
method Diffusion models as Euler-Maruyama integrators for Langevin dynamics, learning forces from static snapshots.
result Diffusion models generate molecular trajectories with temporal correlations similar to MD simulations.
Generative diffusion models are analyzed for their information dynamics.
problem Lack of a unified theoretical understanding of generative diffusion models.
method Integrated perspective connecting information-theoretic, dynamical, and thermodynamic aspects.
result Generative bandwidth is directly governed by the divergence of the score function's vector field.
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.
CDLF predicts product life-cycles in cold-start phases with high accuracy.
problem Forecasting new products in early phases when data is scarce.
method Conditional Diffusion Life-cycle Forecaster (CDLF) combining static descriptors, reference trajectories, and new observations.
result CDLF outperforms classical models in accuracy and probabilistic forecasting.
EntroPath learns manifold geometry from diffusion paths.
problem Learning geodesic geometry from data graphs with spurious shortcuts.
method Maximum Entropy Path Ensemble Embedding (MERW) with k-step diffusion paths.
result EntroPath converges to squared geodesic distance in the short-time limit.
Improves diversity of text-to-image models without sacrificing FID.
problem Lack of diversity and tendency to recreate training set images.
method Adds sparse repellency terms to diffusion SDE to guide trajectories away from a reference set.
result Improves diversity of diffusion models with minimal impact on FID.
Extends diffusion-based Schrödinger bridge models to handle time-dependent potentials.
problem Approximating optimal transport dynamics between two boundary distributions with a twisted Brownian motion reference.
method Introduces Twisted Schrödinger Bridge Matching (TSBM) using the Iterative Markovian Fitting (IMF) paradigm, incorporating a gradient-dependent bridge-matching loss.
result Improves trajectory inference across high-dimensional settings, including crowd navigation and single-cell data.
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.
problem Understanding and quantifying the TV distance between solutions of kinetic Langevin diffusions with different initial values.
method Established new non-Markovian couplings for kinetic Langevin diffusions, derived from optimal coalescence trajectories, and analyzed their TV bounds.
result No Markovian coupling can capture the asymptotic decay rate of the TV distance between solutions of kinetic Langevin diffusions with different initial values.
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order, that consistently generalizes previously proposed pro…
Framework learns continuous dynamics from sparse trajectories.
problem Learning dynamics from sparsely sampled and high-dimensional trajectories.
method Interpolative Multi-Marginal Flow Matching (IMMFM) framework.
result IMMFM outperforms existing methods in forecasting and downstream tasks.
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.
It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with cadlag paths and propose a scheme for computing…
Method detects trajectory outliers using Hodge Laplacian embeddings.
problem Detecting outliers in trajectory data on simplicial complexes.
method Flow-embeddings using Hodge 1-Laplacian of simplicial complexes.
result Classifies trajectories based on topological behavior.
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.
Bi-Mamba model predicts diffusion coefficients and exponents from short data.
problem Characterizing anomalous diffusion in complex systems.
method Bidirectional state-space deep learning architecture.
result Efficient inference of diffusion coefficient and exponent from short trajectories.
CODA resolves coordination issues in offline multi-agent reinforcement learning.
problem Coordination failure in offline multi-agent reinforcement learning.
method Diffusion-based multi-agent trajectory generator for data augmentation.
result CODA resolves coordination pathologies in continuous polynomial games and complex benchmarks.
Paper uses RL and diffusion models to solve Bayesian inverse problems.
problem Bayesian inverse problems with latent biases.
method Relative Trajectory Balance (RTB) for RL, conditional diffusion models, off-policy backtracking exploration.
result RTB improves diffusion model posteriors for inverse problems.
Algorithm learns stochastic system dynamics from data.
problem Recovering interpretable symbolic expressions for stochastic systems.
method Data-driven, trajectory averaging, drift-informed correction.
result Recover coefficients and densities to within 5% and 0.01 in total variation, respectively.
GDB bridges geometric states with improved accuracy and generality.
problem Challenges in predicting geometric state evolution in complex systems.
method Geometric Diffusion Bridge (GDB) framework using equivariant diffusion bridges.
result GDB surpasses existing methods in accurately bridging geometric states.
Training-free model learns SDE dynamics without training, accelerating parameter studies.
problem High computational cost of simulating parameter-dependent SDEs.
method Training-free conditional diffusion model with joint kernel-weighted Monte Carlo estimator.
result Accurate approximation of conditional distributions across varying parameter values.
Diffusion models enhance robotic manipulation through probabilistic multi-modal learning.
problem Enhancing robotic manipulation through robust and multi-modal learning.
method Probabilistic diffusion models integrating imitation and reinforcement learning.
result Diffusion models improve grasp learning, trajectory planning, and data augmentation in robotics.
Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availabi…
The paper analyzes sampling and estimation on manifolds using Langevin diffusion.
problem Sampling and estimation on compact Riemannian manifolds.
method Discretization of Langevin diffusion with error bounds derived.
result First-order error bounds for bias and variance in estimators.
DYffusion improves diffusion models for spatiotemporal forecasting.
problem Challenges in generating stable and accurate forecasts for dynamic data.
method Leverages temporal dynamics in data, directly coupling it with diffusion steps.
result Improves computational efficiency and performs competitively on complex dynamics.
DEMOTE uses neural diffusion-reaction processes to capture temporal dynamics in sparse tensor data.
problem Sparse and temporally associated tensor data with limited structural knowledge.
method Develops a neural diffusion-reaction process to estimate dynamic embeddings for tensor modes.
result Captures both commonalities and personalities in evolving tensor entries.
Single-step samplers generate high-quality samples efficiently.
problem Sampling from unnormalized distributions is computationally expensive.
method Developed consistent diffusion samplers that generate samples in a single step.
result Single-step samplers produce high-fidelity samples with less than 1% of traditional samplers' evaluations.
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.