A new variational inference method uses neural networks to tilt Lévy measures, enabling scalable posterior inference for jump processes while preserving their discontinuous structure.
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Neural Stochastic Differ- ential Equations: Deep Latent Gaussian Models in the Diffu- sion Limit
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FTM learns the probability current velocity from trajectories to deliver fast, trajectory-aware ensemble predictions for stochastic dynamical systems and PDEs.
Extends robust MDPs to continuous time with policy gradient derivations using differential equation methods and proposes optimizers achieving linear convergence and specific sample complexities.
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 outperforms naive integration in ablations.
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.
DiffeoMorph learns distributed agent protocols to morph into complex 3D shapes from minimal initial conditions via equivariant GNNs and rotation-invariant Zernike loss.
A new shared video-image tokenizer enables large language models to surpass diffusion models on standard visual generation benchmarks.
Imagen Video generates high-definition text-conditional videos via a cascade of base and super-resolution diffusion models, achieving high fidelity and controllability.
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.
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 on video prediction and unconditional generation benchmarks.
Progressive distillation halves sampling steps repeatedly in diffusion models, reaching 4 steps with FID 3.0 on CIFAR-10 from 8192-step samplers.
PC-MambaSDE combines Mamba with physics-constrained SDE for RUL prediction under irregular observations, with theoretical stability guarantees and empirical outperformance on benchmarks.
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.
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 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.
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 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.
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.
A conceptual discussion clarifying the roles of aleatoric and epistemic uncertainty when modeling dynamical systems across ML tasks.
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.
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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.
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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.
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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.
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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 outperforms naive integration in ablations.
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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.
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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.
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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.
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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.
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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 on video prediction and unconditional generation benchmarks.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.