New method DDVI improves posterior inference for deep Gaussian processes.
problem Inference of inducing points in DGPs is challenging and biased.
method DDVI uses denoising diffusion SDE and score matching for posterior approximation.
result Empirically shows DDVI outperforms baseline methods in inducing point inference.
When the parameters are independently and identically distributed (initialized) neural networks exhibit undesirable properties that emerge as the number of layers increases, e.g. a vanishing dependency on the input and a concentration on restrictive families of functions including constant functions. We consider parame…
A new criterion for deep active learning selects minimal labeled data points.
problem Efficiently select minimal labeled data points for deep neural networks.
method Diffuses label information over a graph of data representations to switch between exploration and refinement.
result The diffusion-based criterion outperforms existing methods in deep active learning.
Develops RL for optimal market-making in non-Markov processes.
problem Optimal market-making in non-Markov price processes.
method Deep reinforcement learning with Soft Actor-Critic (SAC) algorithm.
result Optimal strategy for market-making in semi-Markov and Hawkes Jump-Diffusion dynamics.
DDP models dynamic comorbidity networks from event data.
problem Understanding complex temporal patterns of co-occurring diseases.
method Developed deep diffusion processes (DDP) to model dynamic comorbidity networks.
result DDP enables accurate risk prediction and interpretable disease trajectories.
Extends RDS filtering to position-orientation space for better image processing.
problem Enhancing and inpainting images with crossing structures.
method Created a version of RDS filtering using gauge frames, studying generalised diffusion.
result RDS filtering on position-orientation space improves denoising and inpainting of crossing structures.
Backpropagation is explained as a diffusion process in neural networks.
problem The biological plausibility of Backpropagation is questioned.
method Demonstrated that time-delayed neurons and forward-backward waves approximate the gradient in deep networks.
result Backpropagation can be interpreted as a diffusion process, approximating the gradient for non-fast inputs.
Diffusion models reveal a phase transition in reconstructing high-level features.
problem Understanding the hierarchical structure of natural data.
method Study of hierarchical generative models of data using diffusion models.
result The backward diffusion process shows a phase transition at a threshold time, where high-level features suddenly drop in reconstructibility.
This paper extends ResNet theory to infinitely deep networks, linking them to diffusion processes.
problem Training infinitely deep ResNets with i.i.d. initializations leads to undesirable properties.
method Introduced doubly infinite ResNets with i.i.d. initializations, linking to diffusion processes.
result The dynamics of quantities of interest converge to deterministic limits in the limit of infinite depth.
There are many real-world knowledge based networked systems with multi-type interacting entities that can be regarded as heterogeneous networks including human connections and biological evolutions. One of the main issues in such networks is to predict information diffusion such as shape, growth and size of social even…
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. This work considers the diffusion limit of suc…
Deep neural network detects asset bubbles with improved accuracy.
problem Detecting asset bubbles in financial markets.
method Developed a deep learning neural network to estimate diffusion coefficient of price processes.
result Improved detection of asset bubbles compared to existing methods.
Studying SGD on deep neural networks using diffusion maps.
problem Understanding why SGD performs well in deep learning.
method Data-driven approach using diffusion maps to analyze SGD dynamics.
result SGD dynamics may mainly live on a low-dimensional manifold in high-dimensional parameter space.
Improved diffusion bridge sampling with rKL-LD loss.
problem Improving sampling from unnormalized distributions using diffusion bridges.
method Employing the rKL-LD loss instead of the Log Variance (LV) loss for diffusion bridges.
result rKL-LD consistently outperforms LV loss in diffusion bridges.
Deep learning dynamics exhibit anomalous superdiffusion initially, aiding escape from local minima.
problem Understanding the dynamics of learning in deep neural networks.
method Novel analysis of SGD dynamics and loss landscape structure.
result SGD exhibits anomalous superdiffusion initially, transitioning to subdiffusion as learning progresses.
Improved sampling via learned diffusions using variational losses.
problem Sampling from target distributions without direct access to samples.
method Generalized Schrödinger bridge problem, variational formulation, gradient-based optimization.
result Proposed log-variance loss leads to improved performance.
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly using the weak form of master equation for probability evolution. In the small ste…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and…
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.
Generative diffusion models mimic biological memory networks, encoding associative dynamics in deep neural weights.
problem Understanding long-term memory mechanisms in neuroscience and AI.
method Interpreting generative diffusion models as energy-based models and comparing them to Hopfield networks.
result Generative diffusion models can encode associative dynamics of Hopfield networks in deep neural weights.
Special issue on understanding physical processes from unusual diffusion patterns.
problem Understanding physical processes from anomalous diffusion data.
method Not explicitly described in the abstract, but likely involves analysis of data from the Anomalous Diffusion Challenge.
result Not explicitly stated, but likely includes analysis of physical processes from anomalous diffusion data.
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.
We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers of probabilistic models that learn to encode the structured information in an in…
We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under different number of layers, neurons per layer, and various different activation fun…
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.
Due to the rapid growth of machine learning tools and specifically deep networks in various computer vision and image processing areas, application of Convolutional Neural Networks for watermarking have recently emerged. In this paper, we propose a deep end-to-end diffusion watermarking framework (ReDMark) which can be…
New method for fast inference in diffusion models.
problem Intractable probabilistic inference in diffusion models.
method Variational Gaussian Process, exponential family description, convex optimization.
result Improved fast algorithm for learning model parameters.
We introduce and study a class of probabilistic generative models, where the latent object is a finite-dimensional diffusion process on a finite time interval and the observed variable is drawn conditionally on the terminal point of the diffusion. We make the following contributions: We provide a unified viewpoint on b…
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.
New method improves OOD detection by integrating diffusion models into discriminator models.
problem Overconfidence in discriminator models leads to poor OOD detection.
method Integrates diffusion models into discriminator and generation models to mitigate overconfidence.
result Demonstrates significant improvement in AUROC scores for challenging datasets.
This work connects diffusion models to power iteration, revealing how low frequencies emerge earlier.
problem Understanding the generation process of diffusion models and their relation to power iteration.
method Examined the linear case of diffusion models, connecting them to the spiked covariance model and power iteration.
result Linear diffusion models converge to the leading eigenvector, similar to power iteration.
Automated denoising score matching handles nonlinear diffusion processes.
problem Nonlinear diffusion processes limit generative modeling and property estimation.
method Local-DSM using local increments and Taylor expansions.
result Tractable training and score estimation for nonlinear diffusion processes.
New method infers and samples point processes from latent diffusion.
problem Modeling point processes with latent diffusion.
method Itô's excursion theory for inference and sampling.
result Proposes a new method to infer and sample point processes.
GRAND treats GNNs as PDE discretizations, addressing graph learning issues.
problem Graph learning issues like depth, oversmoothing, and bottlenecks.
method Models GNNs as a continuous diffusion process, treating them as PDE discretizations.
result Linear and nonlinear versions of GRAND achieve competitive results on graph benchmarks.
In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite the success of recent deep learning methods for diffusion, we find that they often…
A new method uses Gaussian processes and deep kernel learning to price high-dimensional American options efficiently.
problem Challenges in pricing high-dimensional American options, especially with excessive computational costs.
method Modified Gaussian process regression with deep kernel learning and sparse variational Gaussian processes.
result The method outperforms least squares Monte Carlo in high-dimensional scenarios, especially with Merton's jump diffusion model.
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.
We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the span of the sub-Riemannian structure. In the case where the endpoints agree and t…
Extends neural diffusion processes for multi-task regression.
problem Limited to single-task inference, existing formulations cannot capture dependencies across related tasks.
method Introduces a task encoder to condition diffusion model on low-dimensional representations of context observations.
result Improves predictive performance and uncertainty calibration across related functions.
Anomalous diffusion in SGD reveals interactions between hyperparameters and Hessian.
problem Understanding the limiting dynamics of SGD in deep neural networks.
method Continuous-time model of SGD as an underdamped Langevin equation, derived for linear regression.
result Anomalous diffusion is explained by modified loss and probability currents in phase space.
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
FLDD improves discrete diffusion models by learning a non-Markovian noising process.
problem Efficiency and quality of discrete diffusion models in few-step generation.
method Introduces a learnable non-Markovian forward (noising) process to match the target distribution.
result FLDD produces higher quality samples in fewer steps compared to conventional discrete diffusion models.
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.
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.
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.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
Deep neural networks can solve optimal stopping problems without dimensionality issues.
problem Optimal stopping problems in high-dimensional state spaces.
method Established a general framework for deep ReLU neural networks to approximate value functions and continuation values.
result Deep neural networks can approximate value functions and continuation values with error at most ε of size κd^q ε^(-r).
Improves generative models by adding jump-diffusion noise.
problem Limited performance of diffusion models in generating samples from unknown distributions.
method Generalizes diffusion processes to include jump-diffusion noise, deriving closed-form generalized score functions.
result Jump-diffusion models outperform Gaussian models in specific parameter regimes.