REVIEW 29 cited by
Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
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 such models, where the number of layers tends to infinity, while the step size and the noise variance tend to zero. The limiting latent object is an It\^o diffusion process that solves a stochastic differential equation (SDE) whose drift and diffusion coefficient are implemented by neural nets. We develop a variational inference framework for these \textit{neural SDEs} via stochastic automatic differentiation in Wiener space, where the variational approximations to the posterior are obtained by Girsanov (mean-shift) transformation of the standard Wiener process and the computation of gradients is based on the theory of stochastic flows. This permits the use of black-box SDE solvers and automatic differentiation for end-to-end inference. Experimental results with synthetic data are provided.
Forward citations
Cited by 29 Pith papers
-
Variational Inference for L\'evy Process-Driven SDEs via Neural Tilting
A new variational inference method uses neural networks to tilt Lévy measures, enabling scalable posterior inference for jump processes while preserving their discontinuous structure.
-
First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
FTM learns the probability current velocity from trajectories to deliver fast, trajectory-aware ensemble predictions for stochastic dynamical systems and PDEs.
-
Policy Gradient for Continuous-Time Robust Markov Decision Processes
Extends robust MDPs to continuous time with policy gradient derivations using differential equation methods and proposes optimizers achieving linear convergence and specific sample complexities.
-
Towards Continuous-time Causal Foundation Models
Introduces trajectory-law invariance to observation schedule as a continuity criterion for continuous-time causal PFNs, with a three-tier taxonomy and a random-DAG construction using fine-grid integration that outperf...
-
The finite expression method for turbulent dynamics with high-order moment recovery
A two-stage symbolic regression plus generative model framework recovers governing interaction terms and forcing in stochastic triad models while accurately predicting statistical moments up to order five.
-
Pathwise Learning of Stochastic Dynamical Systems with Partial Observations
A neural path estimation approach learns the filtering posterior path measure for stochastic dynamical systems from noisy partial observations by solving a variational stochastic control problem based on the pathwise ...
-
DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations
DiffeoMorph learns distributed agent protocols to morph into complex 3D shapes from minimal initial conditions via equivariant GNNs and rotation-invariant Zernike loss.
-
Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation
A new shared video-image tokenizer enables large language models to surpass diffusion models on standard visual generation benchmarks.
-
Imagen Video: High Definition Video Generation with Diffusion Models
Imagen Video generates high-definition text-conditional videos via a cascade of base and super-resolution diffusion models, achieving high fidelity and controllability.
-
Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding
Imagen achieves state-of-the-art photorealistic text-to-image generation by scaling a text-only pretrained T5 language model within a diffusion framework, reaching FID 7.27 on COCO without training on it.
-
Video Diffusion Models
A diffusion model for video generation extends image architectures with joint image-video training and improved conditional sampling, delivering first large-scale text-to-video results and state-of-the-art performance...
-
Progressive Distillation for Fast Sampling of Diffusion Models
Progressive distillation halves sampling steps repeatedly in diffusion models, reaching 4 steps with FID 3.0 on CIFAR-10 from 8192-step samplers.
-
Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations
PC-MambaSDE combines Mamba with physics-constrained SDE for RUL prediction under irregular observations, with theoretical stability guarantees and empirical outperformance on benchmarks.
-
The Transformer as a Polar State Estimator
The paper casts the standard Transformer block with RoPE as a first-order approximation of a radial–tangential state estimator and introduces a Polar Transformer variant that retains the discarded geometric corrections.
-
The Transformer as a Polar State Estimator
The standard Transformer block arises as a first-order approximation to a polar state estimator on the hypersphere, with a Polar Transformer retaining higher-order terms.
-
The Transformer as a Polar State Estimator
Transformer components arise as the natural solution to precision-weighted directional state estimation on the hypersphere.
-
Variational Smoothing and Inference for SDEs from Sparse Data with Dynamic Neural Flows
A variational method learns a neural approximation to the conditional backward-in-time score of the posterior SDE, inducing an ELBO for joint smoothing and parameter learning from sparse data.
-
Neural Stochastic Processes for Satellite Precipitation Refinement
NSP model fuses satellite and gauge data with neural processes and SDEs, outperforming 13 baselines and JAXA's operational product on a new 43k-sample US benchmark across six metrics.
-
MIOFlow 2.0: A unified framework for inferring cellular stochastic dynamics from single cell and spatial transcriptomics data
MIOFlow 2.0 learns stochastic cellular trajectories from transcriptomics data via neural SDEs, unbalanced optimal transport for growth, and a joint latent space unifying gene expression with spatial features.
-
Pathwise Learning of Stochastic Dynamical Systems with Partial Observations
A pathwise Zakai-equation control formulation is used to train conditional neural SDEs that amortize nonlinear filtering of partially observed stochastic dynamics.
-
Data-to-Energy Stochastic Dynamics
A new data-to-energy iterative proportional fitting algorithm trains Schrödinger bridges when endpoint distributions are known only through unnormalised densities.
-
Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regions
Stein Diffusion Guidance corrects approximate posteriors in diffusion sampling via a Stein variational mechanism and surrogate SOC objective to enable effective guidance beyond high-density regimes.
-
Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations
Neural mean-field games integrate mean-field game theory with neural SDEs to learn strategic interactions from data in a model-free way, demonstrated on games and viral dynamics.
-
Fourier Neural Operators for Non-Markovian Processes:Approximation Theorems and Experiments
A mirror-padded Fourier neural operator can approximate, with proven error bounds, solution maps of path-dependent SDEs and Lipschitz transformations of fractional Brownian motion.
-
Finite Expression Method with TranNet-based Function Learning for High-Dimensional Partial Differential Equations
An extension of the finite expression method using TranNet-initialized shallow neural operators is proposed as an effective solver for high-dimensional partial differential equations.
-
Numerical PDE solvers outperform neural PDE solvers
DeepFDM, a differentiable finite-difference solver that learns PDE coefficients, achieves 10 to 40 times lower error than FNO, U-Net and ResNet on five scalar time-dependent PDEs in one to three dimensions.
-
What Uncertainties Do We Need for Dynamical Systems?
A conceptual discussion clarifying the roles of aleatoric and epistemic uncertainty when modeling dynamical systems across ML tasks.
-
Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming
This perspective paper categorizes hybrid architectures for combining mechanistic and data-driven models using residual learning, Neural ODEs, and solver-in-the-loop to model neurological disorder progression.
-
Deep Neural Networks Inspired by Differential Equations
A review of differential-equation-inspired neural networks that compiles known results into a taxonomy, with no new experiments or theory.
Discussion (0). Sign in to comment.