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.
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48 results for “diffusion algebras”
On the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebrasmath.DG
The paper examines differential smoothness in specific algebra types.
problem Differential smoothness in 3D skew polynomial algebras and diffusion algebras.
method Analyzes the properties of 3D skew polynomial algebras and diffusion algebras.
result Provides insights into the differential smoothness of these algebra types.
High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical me…
Generalized diffusion type equations are considered and point symmetry analysis is applied to them. The equations with extremal order point symmetry algebras are described. Some old geometrical results are rederived in connection with theory of these equation.
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curv…
Study quantum diffusion on spectral triples and spinor bundles.
problem Characterize quantum diffusion on almost commutative spectral triples.
method Spin geometry, C *-Dirichlet forms, quantum stochastic flows.
result Existence of covariant quantum stochastic flows on spinor bundles.
New model learns graph spectra accurately, outperforming existing methods.
problem Graph diffusion models struggle to distinguish certain graph families and their spectra.
method Leveraged random matrix theory to analytically extract spectral properties, introducing Dyson Diffusion Model.
result Dyson Diffusion Model learns graph spectra accurately and outperforms existing models.
Computing Diffusion Geometrymath.DG
New framework for diffusion geometry simplifies complex calculations.
problem Challenges in applying calculus and geometry to real data.
method Reformulates calculus and geometry via diffusion processes.
result Improves precision, robustness, and computational efficiency.
Geometric formalism views optimization algorithms as discrete connections, revealing their algebraic curvature and flatness properties.
problem Understanding and optimizing the behavior of iterative optimization algorithms.
method Introducing a geometric and operator-theoretic formalism where optimization algorithms are encoded by coupled channels (drift and diffusion) whose algebraic curvature measures the deviation from ideal reversibility.
result Flat connections correspond to methods whose updates commute up to higher order, achieving minimal numerical dissipation and preserving stability.
The paper develops stochastic methods on geometric spaces for transformations.
problem Existence and uniqueness of stochastic processes on geometric spaces.
method Stochastic parallel transport and equivariant diffusions on the group of diffeomorphisms.
result Existence and uniqueness of stochastic parallel transport and equivariant diffusions.
Paper introduces a fast, robust, scalable method for detecting changes in data streams.
problem Detecting changes in data streams efficiently and reliably.
method Bayesian online changepoint detection with provable robustness and scalability.
result The proposed method is more than 10 times faster than previous approaches and provides provable robustness.
Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.
problem Pricing American options in models with time-dependent and exponential jumps.
method Generalizes existing methods for barrier and American options to handle arbitrary time dependencies and solves the problem through algebraic and Fredholm-Volterra equations.
result Presents a semi-analytic solution for American options in time-dependent jump-diffusion models with exponential jumps.
Algorithm learns mixtures of Gaussians efficiently using diffusion models.
problem Learning mixtures of Gaussians with identity covariance.
method Analytic approach using diffusion models to learn score functions.
result Quasi-polynomial time and sample complexity for learning mixtures.
The paper formalizes how concepts are encoded in text-guided generative models and provides a method to manipulate them.
problem Encoding and manipulating concepts in text-guided generative models.
method Formalizing concepts as subspaces of a representation space, developing algebraic manipulation methods.
result The ability to manipulate concepts in generative models through algebraic operations on the representation.
The purpose of this paper is to give a new proof of results of Moscovici and Stanton on the orbital integrals associated with eta invariants on compact locally symmetric spaces. Moscovici and Stanton used methods of harmonic analysis on reductive groups. Here, we combine our approach to orbital integrals using the hypo…
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.
A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limitmath.AP
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 extrapolates spectral densities from smaller models to larger ones.
problem Limited practical computations for large machine learning models.
method Algebraic spectral curve theory for free decompression.
result Framework enables extrapolation of spectral densities with multiple or multi-modal bulks.
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.
An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcs.LG
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.
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.
Discretizes diffusions and harmonic functions on covering spaces.
problem Harmonic functions on covering spaces with bounded growth.
method Lyons-Sullivan discretizations of diffusion operators.
result Equivalence of discretized and continuous harmonic functions.
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 Diffusioncs.LG
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.
Rex solves the inverse problem for ODE/SDE solvers, improving precision and stability.
problem Inversion of ODE/SDE solvers is inaccurate and impractical for precision applications.
method Rex uses Lawson methods to convert explicit Runge-Kutta schemes into algebraically reversible ones.
result Rex achieves near-machine-precision reconstruction and improves generative models.
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.
Diffusion Boosted Treesstat.ML
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.