Quaternionic Brownian motion on flag manifold linked to sphere diffusion.
problem Modeling quaternionic stochastic areas on quaternionic flag manifolds.
method Relating quaternionic Brownian motion to symplectic Brownian motion and using radial dynamics.
result Quaternionic stochastic areas follow a multivariate normal distribution.
Diffusion means converge to extrinsic means for long times on spheres.
problem Understanding the long-time behavior of diffusion means on manifolds.
method Introduced diffusion means as a parameterized family of location statistics on manifolds, and analyzed their convergence to extrinsic means for long times.
result For real projective spaces and connected compact symmetric spaces, the long-time limit of diffusion means is conjectured to be the extrinsic mean in the isometric embedding.
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.
We consider closed immersed hypersurfaces evolving by surface diffusion flow, and perform an analysis based on local and global integral estimates. First we show that a properly immersed stationary (ΔH \equiv 0) hypersurface in \R^3 or \R^4 with restricted growth of the curvature at infinity and small total tracefree c…
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses t…
Efficient diffusion model for symmetric manifolds reduces training and computation costs.
problem Heat kernel computations for manifold diffusion models are computationally expensive and infeasible.
method Spatially-varying covariance diffusion model, efficient objective derived via Ito's Lemma.
result Our model reduces training time and arithmetic operations by orders of magnitude.
In this paper, we propose to adopt the diffusion approximation tools to study the dynamics of Oja's iteration which is an online stochastic gradient descent method for the principal component analysis. Oja's iteration maintains a running estimate of the true principal component from streaming data and enjoys less tempo…
We introduce a fractional Yamabe flow involving nonlocal conformally invariant operators on the conformal infinity of asymptotically hyperbolic manifolds, and show that on the conformal spheres $(\Sn, [g_{\Sn}])$, it converges to the standard sphere up to a Möbius diffeomorphism. This result allows us to obtain extinct…
A new algorithm solves semidefinite programs using Langevin diffusion.
problem Optimizing semidefinite programs with diagonal constraints.
method Langevin diffusion on a product manifold of spheres.
result Langevin algorithm achieves ε accuracy in Ω(ε^-5) iterations.
GDMaps reduces high-dimensional data to lower dimensions for better classification.
problem High-dimensional data classification and representation.
method Grassmannian Diffusion Maps technique for nonlinear dimensionality reduction.
result GDMaps effectively identifies intrinsic subspace structures in high-dimensional data.
We consider a diffuse interface approximation for the lipid phases of rotationally symmetric two-phase bilayer membranes and rigorously derive its Γ-limit. In particular, we prove that limit vesicles are C1 across interfaces, which justifies a regularity assumption that is widely made in formal asymptotic and nume…
The paper proves global existence and convergence of Möbius-invariant Willmore flow in 3-sphere.
problem Global existence and convergence of Möbius-invariant Willmore flow in 3-sphere.
method Use of invariant center manifolds and recent achievements about the Möbius-invariant Willmore flow.
result Fully and smoothly convergent flow lines are stable w.r.t. small perturbations.
Automates learning of multivariate diffusions for generative models.
problem Lack of automated methods for choosing and optimizing diffusion processes in generative models.
method Develops a recipe to maximize likelihood without model-specific analysis, parameterizes diffusion for target noise, and optimizes the inference diffusion process.
result Automatic search over all linear diffusions for generative models.
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
problem Improving the performance of discrete diffusion models.
method Conditioning on the jump schedule of discrete Markov processes.
result Schedule-conditioned discrete diffusion (SCUD) models outperform classical and masking diffusion models.
Diffusion-GAN uses diffusion to improve GAN training stability and realism.
problem Stability and realism issues in training GANs.
method Diffusion-GAN employs a forward diffusion chain to generate Gaussian-mixture distributed instance noise, with adaptive diffusion process and timestep-dependent discriminator.
result Diffusion-GAN produces more realistic images with higher stability and data efficiency.
Study shows how heat leaks from material sets in low diffusivity scenarios.
problem Understanding heat leakage from material sets in low diffusivity limits.
method Generalized leading-order asymptotics for time-dependent diffusion processes.
result Diffusive transport out of a material set is proportional to the surface area of the set boundary.
New blurring diffusion models bridge heat dissipation and denoising.
problem Developing a new generative modeling approach.
method Connecting blurring to Gaussian diffusion with non-isotropic noise.
result Proposed Blurring Diffusion Models offer the best of both Gaussian denoising and inverse heat dissipation.
Study mass transport in low-diffusivity using Lagrangian coordinates.
problem Mass preserving transport of passive tracers in low-diffusivity limit.
method Lagrangian coordinates, time-averaged diffusion equation, weighted manifold structure.
result Leading order asymptotics extend to dominant nontrivial singular value in low-diffusivity limit.
New method tackles video inverse problems using image diffusion models.
problem Spatio-temporal degradation in video inverse problems.
method Leverages image diffusion models to treat time dimension as batch dimension, introduces batch-consistent diffusion sampling.
result Achieves state-of-the-art reconstructions for various spatio-temporal degradations.
Diffusion models generate new samples with active guidance, but theory is limited.
problem Insufficient theoretical understanding of diffusion models.
method Review and progressive routine of diffusion models, including conditional sampling.
result Diffusion models can be used for high-dimensional optimization problems.
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.
PaGoDA reduces diffusion model training costs by 64x.
problem Diffusion models are computationally expensive during training.
method Three-stage pipeline: downsampled training, distillation, progressive super-resolution.
result PaGoDA achieves state-of-the-art performance with reduced training costs.
Study shows diffused interface flows to single diffused balls over time.
problem Volume-preserving mean curvature flow in Euclidean space.
method Diffused interface version, exponential convergence proof.
result Exponential convergence to single diffused balls.
Latent diffusion improves robustness in missing data imputation.
problem Missing data imputation under MCAR corruption.
method Two-stage framework: VAE for latent feature learning, diffusion model in latent space.
result Latent diffusion maintains high quality and stability up to 50% missingness.
The paper examines smoothness in diffusion algebra.
problem Smoothness in diffusion algebras.
method Not explicitly detailed in the abstract.
result Not explicitly detailed in the abstract.
DMPS uses diffusion maps and LAWGD for efficient generative modeling.
problem Efficiently modeling complex data distributions.
method Diffusion maps for manifold learning and LAWGD for sampling.
result DMPS outperforms other methods on moderate-dimensional data.
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
Investor-driven information diffusion affects excess comovement in China and the U.S. markets.
problem Investor-driven information diffusion and its impact on excess comovement.
method Cross-sectional analysis of 4,533 Chinese and 4,517 U.S. stocks from 2010 to 2022.
result Retail-driven information diffusion significantly drives excess comovement in China, while institution-driven diffusion is the primary driver in the U.S.
Diffusion models generate new samples by adding and removing noise.
problem Generating new samples from data.
method Apply noise to data, reverse the process to generate new samples.
result Diffusion models can improve classifier performance on imbalanced data.
Soft Truncation improves diffusion model performance by balancing loss scales across diffusion times.
problem Inverse correlation between density estimation and sample generation in diffusion models.
method Introduces Soft Truncation, a training technique that softens the truncation hyperparameter.
result Soft Truncation achieves state-of-the-art performance on various datasets.
Remasking improves the quality of discrete diffusion models for natural language and image generation.
problem Limited iterative refinement in masked discrete diffusion models.
method Introducing ReMDM sampler that allows remasking during inference.
result Remasking enables better quality outputs with increased sampling steps.
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.
DM uses semigroup property to tune diffusion time for better data analysis.
problem Difficulty in tuning diffusion time for optimal data analysis.
method Proposes a semigroup criterion to select diffusion time.
result Effective and robust method for picking diffusion time.
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.
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
New method bypasses time-reversal for diffusion-based generative models.
problem Diffusion-based generative models require time-reversal, limiting flexibility.
method Constructs diffusion processes without time-reversal through mixtures of diffusion bridges.
result Exact transport without time-reversal, greater flexibility in dynamics.
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.
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.
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.
New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
DBT combines diffusion models and boosting for supervised learning.
problem Supervised learning problems.
method Diffusion Boosting paradigm and Diffusion Boosted Trees (DBT).
result DBT outperforms deep neural network-based diffusion models and is effective on real-world classification tasks.
SJDs unify masked, continuous, and hybrid diffusion models.
problem Unified modeling of diffusion processes.
method Continuous-time Markov processes with token embeddings and hazard rates.
result Unified model recovers masked, continuous, and hybrid diffusion as limits.
Rolling Diffusion improves video prediction by progressively corrupting frames based on their temporal position.
problem Improving video prediction accuracy by accounting for temporal dynamics.
method A sliding window denoising process that assigns more noise to frames that appear later in a sequence.
result Rolling Diffusion outperforms standard diffusion models in tasks with complex temporal dynamics.
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 reweighted losses improve diffusion model training and image quality.
problem Training and improving diffusion models for image generation.
method Constructing a cascade of time-dependent variational lower bounds.
result Significant improvements in pixel-space image modeling quality.
This paper simplifies diffusion models for high resolution images.
problem Applying diffusion models to high resolution images is challenging.
method Adjust noise schedule, scale specific parts, add dropout, and use downsampling.
result Achieved state-of-the-art image generation performance.
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.
Study weak super Ricci flow through neckpinch in metric measure spaces.
problem Understanding Ricci flow behavior at singularities.
method Introduce weak super Ricci flow and show conditions for continuation.
result Weak super Ricci flow properties at singularities.