mlsanityData to 14 Oct 2026

Geometric Trajectory Diffusion Models

arXiv 2410.13027 ↗First posted 16 Oct 2024cs.CV cs.LGcited by 15

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 57 of its 71 references that are in the map. First posted on arXiv 16 Oct 2024.

Builds on

57 of 71 references.

Closest ancestors · 9

Same direction, newest first

  1. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun
  2. 2023Geometric Latent Diffusion Models for 3D Molecule Generation2 May
  3. 2023EigenFold: Generative Protein Structure Prediction with Diffusion Models5 Apr
  4. 2023SE(3) diffusion model with application to protein backbone generation5 Feb
  5. 2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations19 Apr
  6. 2022Equivariant Diffusion for Molecule Generation in 3D31 Mar
  7. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation6 Mar
  8. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  9. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 48

  1. 2017Attention Is All You Needcited by 60,361
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  7. 2018Neural Ordinary Differential Equationscited by 3,779
  8. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  9. 2022Video Diffusion Modelscited by 2,305
  10. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
  11. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,937
  12. 2023Consistency Modelscited by 1,822
36 more
  1. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,136
  2. 2018Self-Attention with Relative Position Representationscited by 1,120
  3. 2022Human Motion Diffusion Modelcited by 1,080
  4. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  5. 2021E(n) Equivariant Graph Neural Networkscited by 965
  6. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  8. 2018Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networkscited by 690
  9. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
  10. 2020Directional Message Passing for Molecular Graphscited by 561
  11. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  12. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  13. 2022PhysDiff: Physics-Guided Human Motion Diffusion Modelcited by 368
  14. 2018Neural Relational Inference for Interacting Systemscited by 339
  15. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 309
  16. 2018SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraintscited by 298
  17. 2022Flexible Diffusion Modeling of Long Videoscited by 294
  18. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  19. 2020It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Predictioncited by 236
  20. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 228
  21. 2022Stochastic Trajectory Prediction via Motion Indeterminacy Diffusioncited by 185
  22. 20233D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Predictioncited by 177
  23. 2021E(n) Equivariant Normalizing Flowscited by 165
  24. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 163
  25. 2021Neural SDEs as Infinite-Dimensional GANscited by 161
  26. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  27. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 76
  28. 2022Equivariant Graph Mechanics Networks with Constraintscited by 68
  29. 2022SocialVAE: Human Trajectory Prediction using Timewise Latentscited by 67
  30. 2021An End-to-End Framework for Molecular Conformation Generation via Bilevel Programmingcited by 59
  31. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  32. 2020BiTraP: Bi-directional Pedestrian Trajectory Prediction with Multi-modal Goal Estimationcited by 47
  33. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 39
  34. 2022Deep Latent State Space Models for Time-Series Generationcited by 38
  35. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 38
  36. 2022Equivariant Graph Hierarchy-Based Neural Networkscited by 24

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 2; 2025: 9; 2026: 4.

15 papers.

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  1. 2025Discrete Diffusion Trajectory Alignment via Stepwise Decompositioncited by 12
  2. 2025STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulationcited by 8
  3. 2025Zero-Shot Cyclic Peptide Design via Composable Geometric Constraintscited by 4
  4. 2024RealTraj: Towards Real-World Pedestrian Trajectory Forecastingcited by 3
  5. 2025Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Spacecited by 3
  6. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  7. 2025PAINET: A Principled Efficient Transformer for 3D Dynamics Modelingcited by 2
  8. 2025GeoAda: Efficiently Finetune Geometric Diffusion Models with Equivariant Adapterscited by 1
  9. 2025CHORDS: Diffusion Sampling Accelerator with Multi-core Hierarchical ODE Solverscited by 1
  10. 2024SEA: State-Exchange Attention for High-Fidelity Physics Based Transformerscited by 0
  11. 2025Follow the MEP: Scalable Neural Representations for Minimum-Energy Path Discovery in Molecular Systemscited by 0
  12. 2026All-Atom GPCR-Ligand Dynamics Simulation via a Residual Latent Flow Modecited by 0
3 more
  1. 2026Align Your Structures: Generating Trajectories with Structure Pretraining for Molecular Dynamicscited by 0
  2. 2026Graph Mamba Operator: A Latent Simulator for Interacting Particle Systemscited by 0
  3. 2026Probabilistic Simulation of Gas-Liquid Interfaces with Coupled Flow Matching on Spherical Harmonicscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Equivariant Flow Matching with Hybrid Probability Transport
  2. 2025Multi-view diffusion geometry using intertwined diffusion trajectories
  3. 2025Equivariant Neural Diffusion for Molecule Generation
  4. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimization
  5. 2025Geometric Regularity in Deterministic Sampling Dynamics of Diffusion-based Generative Models
  6. 2026Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein Dynamics
  7. 2026Probing the Geometry of Diffusion Models with the String Method
  8. 2026GeoSPRINT: Geometric Redundancy-Aware Step Pruning for Inference in Diffusion Trajectories