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.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “Diffusion State Distance”
Establishes a link between heat diffusion and manifold distances in data.
problem No theoretical link between diffusion-based manifold learning and geodesic distances.
method Formulates heat geodesic embeddings based on Riemannian geometry.
result Method outperforms state-of-the-art in preserving manifold distances and cluster structure.
This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.
problem Theoretical guarantees for discrete-state diffusion models remain under-explored.
method Continuous Time Markov Chain (CTMC) framework and discrete-time sampling algorithm.
result Convergence bounds for KL divergence and TV distance are derived, showing linear dependence on dimension.
Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformizationstat.ML
Discrete diffusion models improve data generation for discrete data like language and graphs.
problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.
An unsupervised learning algorithm to cluster hyperspectral image (HSI) data is proposed that exploits spatially-regularized random walks. Markov diffusions are defined on the space of HSI spectra with transitions constrained to near spatial neighbors. The explicit incorporation of spatial regularity into the diffusion…
Efficiently reconstructs jump-diffusion processes from data using neural networks.
problem Reconstructing jump-diffusion processes from data.
method Temporally decoupled squared Wasserstein distance method using parameterized neural networks.
result Enhanced reconstruction of jump-diffusion processes from data.
Paper proves diffusion models work on manifolds.
problem Current diffusion models assume densities are w.r.t. Lebesgue measure, limiting their applicability.
method Introduced convergence results for diffusion models on more general target distributions.
result Quantitative bounds on Wasserstein distance for target and generated distributions.
Study shows diffusion models adapt to manifold hypothesis without dimensionality issues.
problem Empirical success of diffusion models in high-dimensional data.
method Developed a new framework connecting diffusion models to Gaussian Processes theory.
result Achieves rates independent of ambient dimension in terms of score learning and sampling complexity.
LightSBB-M improves generative diffusion modeling with lower 2-Wasserstein distances.
problem Improving generative diffusion models using Schrödinger Bridge and Bass methods.
method Optimizes SBB transport plan with dual representation and tunable beta parameter.
result Achieves up to 32% improvement in 2-Wasserstein distance on synthetic datasets.
Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.
problem Theoretical convergence properties of Brownian motion based diffusion flow matching.
method Refined analysis under Kullback-Leibler and 2-Wasserstein distances.
result State-of-the-art scaling in KL convergence bounds under minimal conditions.
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.
Diffusion models achieve nearly optimal distribution estimation in various spaces.
problem Theoretical limitations of diffusion modeling for distribution estimation.
method Analysis of approximation and generalization abilities of diffusion models in Besov spaces.
result Diffusion models achieve nearly minimax optimal estimation rates in total variation and Wasserstein distances.
New analysis improves convergence guarantees for diffusion-based samplers in Wasserstein distance.
problem Improving convergence guarantees for diffusion-based generative models.
method Simple framework to analyze discretization, initialization, and score estimation errors.
result First Wasserstein convergence bound for the Heun sampler and improved results for Euler sampler.
Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.
problem Challenges in understanding discrete diffusion models on combinatorial state spaces.
method Established convergence bounds for three discrete diffusion models using Euler approximations.
result Optimal non-asymptotic convergence guarantees for discrete diffusion models without boundedness assumptions.
The paper interprets diffusion models as gradient descent and proposes a new sampler.
problem Improving the efficiency and quality of diffusion models.
method Interprets diffusion models as gradient descent and proposes a new sampler.
result The new sampler achieves state-of-the-art FID scores and generates high quality samples.
Existing graph neural networks may suffer from the "suspended animation problem" when the model architecture goes deep. Meanwhile, for some graph learning scenarios, e.g., nodes with text/image attributes or graphs with long-distance node correlations, deep graph neural networks will be necessary for effective graph re…
This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.
problem Improving non-asymptotic bounds for denoising diffusions, especially for the Ornstein-Uhlenbeck process.
method Explicit non-asymptotic bounds on forward diffusion error in total variation, considering multi-modal data distributions.
result The Ornstein-Uhlenbeck process cannot be significantly improved in terms of reducing terminal time for multi-modal data distributions.
New bounds close the score matching gap for diffusion models.
problem The difference between sample quality and score matching loss in diffusion models.
method Theoretical analysis of score matching gap, developing tighter bounds for KL divergence, reverse KL divergence, and Wasserstein distance.
result The quality of score approximation impacts closing the score matching gap for low noise scales.
In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time. The mesh of observations is not required to shrink to zero. As distance between…
Resolving Memorization in Empirical Diffusion Model for Manifold Data in High-Dimensional Spacesstat.ML
Solves memorization in diffusion models for manifold data.
problem Memorization effect in diffusion models for manifold data.
method Inertia update at the end of empirical diffusion simulation.
result Approximates true data distribution on a manifold.
New metrics improve quantum ensemble learning efficiency and power.
problem Quantum ensembles' distances poorly understood due to measurement constraints.
method Introduce MMD- hierarchy of integral probability metrics for quantum ensembles.
result MMD- requires fewer samples for full discriminative power at higher .
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering often rely on some distance or similarity measure. It is of tremendous importance t…
This paper bridges the gap between ODE and SDE in diffusion models using Fokker-Planck equations.
problem Empirical evidence shows that ODE-based samples from score-based diffusion models are inferior to SDE-based samples.
method The paper rigorously describes dynamics and approximations in training score-based diffusion models, linking them to Fokker-Planck equations.
result Adding a regularisation term based on the Fokker-Planck residual can close the gap between ODE- and SDE-induced distributions.
The paper shows diffusion models can converge faster to a target distribution with low-dimensional structure.
problem Improving the convergence rate of diffusion models to target distributions.
method Analyzing DDIM and DDPM samplers under low-dimensional structure assumptions.
result The iteration complexities of DDIM and DDPM are no greater than in total variation distance.
DDPMs are robust to noisy score estimates and achieve optimal convergence rates in Wasserstein-2 distance.
problem Evaluating the quality of DDPMs in Wasserstein distance with noisy score estimates.
method Established finite-sample guarantees in Wasserstein-2 distance for DDPMs, considering noisy score estimates.
result Optimal convergence rates in Wasserstein-2 distance for DDPMs, matching Gaussian case.
CDM models counterfactual outcomes in longitudinal data with improved accuracy.
problem Predicting counterfactual outcomes in longitudinal data with complex time-dependent confounding.
method Causal Diffusion Model (CDM) using denoising diffusion architecture with relational self-attention.
result CDM outperforms state-of-the-art methods in generating full probabilistic distributions of counterfactual outcomes.
Diffusion models adapt to low-dimensional data regardless of coefficient choices.
problem Understanding how diffusion models adapt to low-dimensional data structures.
method Analysis of diffusion models with flexible coefficient choices.
result Proven that iterations suffice for accurate sampling in total variation distance.
Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transportcond-mat.stat-mech
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.
FDBM models use fractional Brownian motion to model complex stochastic processes.
problem Capturing memory effects and long-range dependencies in stochastic processes.
method Developed a generative diffusion bridge framework using a Markovian approximation of fractional Brownian motion.
result FDBM outperforms standard models in predicting future states and unpaired data translation.
Paper introduces a new generative learning model using Schrödinger bridge diffusion in latent space.
problem Learning distributions from divergent data distributions.
method Pre-training with large-scale models, Schrödinger bridge diffusion model in latent space.
result Effective control of second-order Wasserstein distance between generated and target distributions.
A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.
problem Understanding what a discrete diffusion model learns in different coordinate systems.
method Rigorous derivation of continuous-time Markov chain ELBO, Oracle Distance theorem, and exact coordinates for optimizer.
result The negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one.
In this paper, we propose a novel approach for manifold learning that combines the Earthmover's distance (EMD) with the diffusion maps method for dimensionality reduction. We demonstrate the potential benefits of this approach for learning shape spaces of proteins and other flexible macromolecules using a simulated dat…
New sampling method improves efficiency for diffusion models.
problem Efficient sampling from arbitrary smooth distributions in polynomial time.
method Randomized midpoint method for log-concave sampling.
result Achieves best known dimension dependence () for total variation distance.
Starting from a sequence of independent Wright-Fisher diffusion processes on , we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in Let $Mμ\ff 1 2\DD+ZZ$…
QTD integrates quantization with diffusion for efficient data generation.
problem Challenges in continuous diffusion models, especially long-range transitions and biases.
method Quantized Transition Diffusion (QTD) integrates data quantization with discrete diffusion dynamics.
result QTD achieves efficient data generation with minimal score evaluations.
Deep Bootstrapstat.ML
A novel deep bootstrap framework for nonparametric regression using conditional diffusion models.
problem Nonparametric regression with efficient sampling and accurate estimation.
method Conditional diffusion model for learning conditional distributions, integrating sampling and regression into a unified generative framework.
result Established optimal convergence rates in the Wasserstein distance and convergence guarantees for the bootstrap procedure.
We analyze a new Markov chain model for better sampling and optimization.
problem Developing a new Markov chain model for improved sampling and optimization.
method We introduce a new class of Ito chains with arbitrary noise and inexact drift/diffusion coefficients, proving a bound in -distance.
result Our analysis provides improved or first results for various applications like SGLD, sampling, and boosting.
New framework for discrete-state diffusion models reduces sample complexity.
problem Lack of theoretical understanding and sample complexity analysis for discrete-state diffusion models.
method Developed a principled theoretical framework, decomposing score estimation error.
result Established sample complexity bound of .
Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often insufficient for visualizing the global and local structure of the data. In thi…
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of distributions with densities that are both multimodal and have nonlinear shapes. A crucial …
LACD uses unlabeled data to improve conditional diffusion models.
problem Costly and time-consuming acquisition of labeled data.
method Label-augmented conditional diffusion (LACD) with joint denoising score matching.
result LACD converges faster in total variation and Wasserstein-1 distances with sufficient unlabeled data.
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.
Diffusion models adapt to low-dimensional structures for nonparametric density estimation.
problem High-dimensional statistical inference challenges.
method Viewing diffusion models as implicit density estimators and exploiting their low-dimensional structure.
result Achieves minimax optimal rate for total variation distance with factorizable density.
New theory improves diffusion model convergence for generating data.
problem Improving convergence of diffusion models for data generation.
method Developed a non-asymptotic convergence theory for probability flow ODEs.
result Proves iterations suffice for approximating target distributions.
KIPLMC methods improve statistical inference in latent variable models.
problem Statistical inference in latent variable models.
method Joint diffusion process in parameter and latent variable spaces, with two explicit discretizations.
result KIPLMC methods achieve accelerated convergence rates in Wasserstein-2 distance.
Combines deep state space models with diffusion models for better forecasting and capturing latent dynamics
problem Forecasting and capturing latent dynamics in time series
method DDSSM: Diffusion-driven state space model
result Empirically outperforms state-of-the-art deep SSM
Improved error estimate for SGLD sampling algorithm.
problem Establishing a precise error bound for SGLD.
method Sharp uniform-in-time error estimate for SGLD under mild assumptions.
result Uniform-in-time bound for KL-divergence between SGLD and Langevin diffusion.
Flow Matching improves Wasserstein 1 distance convergence in high dimensions.
problem Improving Wasserstein 1 distance estimation for unbounded distributions.
method Flow Matching approach based on ODEs, controlling Lipschitz constant.
result Derives a convergence rate for Wasserstein 1 distance, improving previous results.