Reconstructs Riemannian geometry from diffusion properties.
problem Recovering Riemannian geometry from diffusion data.
method Intrinsic reconstruction from diffusion semigroup and calculus.
result Reveals Riemannian structure from diffusion properties.
Researchers interpret SGD using diffusion metrics for clearer geometric understanding.
problem Elusiveness of geometrical significance in stochastic gradient descent.
method Study a deterministic model with geodesics of diffusion metrics.
result Establishes parallel with General Relativity models.
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 compares PINN methods for solving drift-diffusion equations on metric graphs.
problem Solving drift-diffusion equations on metric graphs using machine learning.
method Comparison of physics-informed neural networks (PINNs) for solving drift-diffusion equations on metric graphs.
result PINNs offer a flexible and versatile tool for solving parameter identification or optimization problems on metric graphs.
Develops DSD for analyzing multiscale biological networks.
problem Analyzing multiscale structure in biological networks.
method Data-driven diffusion process with multitemporal analysis.
result Parameter-free inference of intrinsic data structure.
Study explores efficient continual learning of diffusion models.
problem Efficiently reusing computation in training diffusion models as data evolves.
method Benchmarked and analyzed CL methods for Denoising Diffusion Probabilistic Models (DDPMs).
result Experience replay with reduced rehearsal coefficient shows strong performance.
Survey of diffusion models for time series forecasting.
problem Lack of systematic taxonomy for diffusion models in time series forecasting.
method Introduction and review of standard diffusion models, their variants, and their adaptation to time series tasks.
result Provides a comprehensive categorization and summary of diffusion models for time series forecasting.
Statistical analysis of Diffusion Tensor Imaging (DTI) data requires a computational framework that is both numerically tractable (to account for the high dimensional nature of the data) and geometric (to account for the nonlinear nature of diffusion tensors). Building upon earlier studies that have shown that a Rieman…
This paper improves QoS metric prediction in DTNs using diffusion models.
problem Improving QoS metric prediction in Delay-Tolerant Networks (DTNs) to enhance network performance.
method Formulates QoS metric prediction as a probabilistic forecasting problem on multivariate time series, incorporating latent temporal dynamics.
result The proposed approach outperforms traditional methods in QoS metric prediction for DTNs.
Enhances geodesic fiber tracking in white matter using modified metrics and tensor data.
problem Improving the accuracy and robustness of geodesic fiber tracking in white matter.
method Modification of geodesic ray-tracing method using rescaled metrics and fourth-order tensor data.
result More satisfactory results in the construction of white matter tracts as geodesics.
Theoretical analysis shows MDMs can be efficient but not for all metrics.
problem Understanding the efficiency-accuracy trade-off of diffusion language models.
method Theoretical analysis of Masked Diffusion Model (MDM) using perplexity and sequence error rate as metrics.
result MDM achieves near-optimal perplexity but requires linear scaling for sequence error rate, highlighting efficiency-accuracy trade-offs.
We consider the problem of constructing diffusion operators high dimensional data X to address counterfactual functions F, such as individualized treatment effectiveness. We propose and construct a new diffusion metric KF that captures both the local geometry of X and the directions of variance of F. The res…
The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
problem Gradient estimates for porous medium and fast diffusion equations on metric measure spaces.
method Derives Li-Yau and Souplet-Zhang type gradient estimates for the given equations.
result Gradient estimates for the equations on complete noncompact metric measure spaces with compact boundary.
Paper analyzes latent space geometry in generative models using Fisher information.
problem Understanding the structure of latent spaces in generative models.
method Reconstructs Fisher information metric from generated samples and posterior distribution.
result Reveals fractal structure and abrupt changes in Fisher metric at phase boundaries.
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
We propose a family of near-metrics based on local graph diffusion to capture similarity for a wide class of data sets. These quasi-metametrics, as their names suggest, dispense with one or two standard axioms of metric spaces, specifically distinguishability and symmetry, so that similarity between data points of arbi…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interp…
New method learns discrete graph diffusion via free-energy gradient flows.
problem Challenges in translating continuous diffusion models to discrete spaces.
method Proposes a novel computational approach using a specific metric on the simplex.
result Recover the underlying functional for various graph classes.
Geodesic walks converge to Brownian motion on Finsler manifolds.
problem Understanding random walks on Finsler manifolds.
method Analyzing convergence of geodesic random walks to diffusion processes.
result The Brownian motion on a Riemannian metric is a key result.
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.
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.
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.
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.
LADD models improve discrete diffusion for faster language generation.
problem Practical discrete diffusion models ignore cross-token dependencies, degrading performance.
method Introduces a learnable auxiliary latent channel, diffusing over the joint (token, latent) space.
result LADD models yield improvements on unconditional generation metrics.
Improved sampling in generative models using CLDs with a hyperparameter.
problem Improving sampling performance in generative models.
method Extending Critically-damped Langevin Diffusions with a hyperparameter to control noise.
result Derivation of a novel upper bound on Wasserstein sampling error.
Study on removing sets and uniqueness of diffusion operators on various spaces.
problem Determining the effect of removing small sets on the self-adjointness and uniqueness of diffusion operators.
method Analyzes symmetric diffusion operators on metric measure spaces, proving a truncation result for potentials.
result Characterizes the critical size of removed sets and their effect on operator properties.
A new model for point processes without intensity function trade-offs.
problem Inefficiency and trade-offs in existing point process models.
method Point Set Diffusion, a diffusion-based latent variable model.
result Achieves state-of-the-art performance in point process generation.
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.
This paper establishes a theoretical foundation for consistency training in diffusion models.
problem Lack of a comprehensive theoretical understanding of consistency training in diffusion models.
method Demonstrates the necessity of a number of steps in consistency learning exceeding d5/2/ε for generating samples within ε proximity to the target distribution. result Establishes rigorous insights into the validity and efficacy of consistency models, offering theoretical underpinnings for their utility.
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.
This research explores how different discrete diffusion kernels affect graph generation quality.
problem The impact of different discrete diffusion kernels on graph generation quality.
method Developed a family of discrete diffusion kernels that converge to different Bernoulli priors.
result The quality of generated graphs is sensitive to the prior used, challenging previous intuitions.
Study flaws in generative model evaluation metrics, especially for diffusion models.
problem Flaws in existing metrics for evaluating generative models, particularly for diffusion models.
method Systematic study of generative models, human perception experiments, and analysis of feature extractors.
result State-of-the-art perceptual realism of diffusion models is not reflected in commonly reported metrics.
This work proposes a geometric approach to equivariant message passing on Riemannian manifolds.
problem Efficiently processing data on Riemannian manifolds with equivariance.
method Geometric insight into equivariant message passing on Riemannian manifolds, using an equivariant embedding and diffusion process.
result A new class of equivariant GNNs on Riemannian manifolds.
A new method for signal recovery in high dimensions using projections and diffusion models.
problem Recovering a latent signal from noisy observations with unknown support.
method Metric projection estimator based on score matching in a diffusion model.
result The posterior distribution concentrates near the metric projection of the observed signal.
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
We study the problem of non-explosion of diffusion processes on a manifold with time-dependent Riemannian metric. In particular we obtain that Brownian motion cannot explode in finite time if the metric evolves under backwards Ricci flow. Our result makes it possible to remove the assumption of non-explosion in the pat…
Generative diffusion models improve channel sampling from limited data.
problem Challenges in channel modelling and data collection for wireless systems.
method Diffusion model with U-Net architecture for frequency domain synthesis.
result Stable training and diverse high-fidelity samples generated from true channel distribution.
Paper defends diffusion models from membership inference attacks using Langevin dynamics.
problem Defending diffusion models against membership inference attacks.
method Uses critically-damped higher-order Langevin dynamics with auxiliary variables.
result Demonstrates improved resistance to membership inference attacks through theoretical investigation and validation.
Self-play fine-tuning improves diffusion models for text-to-image generation.
problem Plateauing performance of diffusion models after data saturation.
method Self-play fine-tuning (SPIN-Diffusion) using competition among model versions.
result Significantly improved model performance and human preference alignment.
This work improves diffusion models by estimating the optimal loss value for better training diagnostics.
problem The optimal loss value of diffusion models is unknown and not indicative of absolute data-fitting quality.
method Derive the optimal loss in closed form and develop effective estimators, including a stochastic variant.
result Unlocking the optimal loss as a metric for diagnosing training quality of diffusion models.
Tutorial on optimizing diffusion model samples for specific metrics.
problem Optimizing diffusion model samples for specific downstream metrics.
method Review and exploration of inference-time guidance and alignment methods.
result Unified perspective on inference-time algorithms and novel methods.
GEOMANCER learns manifold factors without supervision.
problem Learning to factorize Lie group orbits from data.
method Subspace diffusion estimation of invariant subspaces.
result Unsupervised disentanglement of complex manifolds possible.
This paper analyzes sampling from heavy-tailed distributions using discretized Itô diffusions.
problem Sampling from heavy-tailed distributions with finite variance.
method Mean-square analysis of discretized Itô diffusions with weighted Poincaré inequalities.
result Explicit iteration complexity for obtaining samples close to target distributions in Wasserstein-2 metric.
Paper presents a new video generation model using diffusion probabilistic methods.
problem Generating high-quality video sequences.
method Denoising diffusion probabilistic models, autoregressive, end-to-end optimization.
result Significant improvements in perceptual quality and probabilistic frame forecasting.
We characterize lower bounds for the Bakry-Emery Ricci tensor of nonsymmetric diffusion operators by convexity of entropy on the L2-Wasserstein space, and define a curvature-dimension condition for general metric measure spaces together with a square integrable 1-form in the sense of \cite{giglinonsmooth}. This ex…
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.
A new diffusion model uses efficient conditional estimators for discrete data.
problem Efficient estimation of conditional probabilities for discrete data.
method Discrete denoising diffusion framework with sample-efficient NeurISE conditional estimation.
result The method outperforms existing approaches in various metrics on binary and scientific data.
Enhances RL in partially observable, noisy environments by uncovering causal states.
problem Making decisions based on incomplete and noisy observations in partially observable Markov decision processes (P2OMDPs). method Causal State Representation under Asynchronous Diffusion Model (CaDiff) framework, incorporating a novel asynchronous diffusion model (ADM) and a new bisimulation metric.
result Enhances returns by at least 14.18% compared to baselines on Roboschool tasks.