# MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation

arXiv: https://arxiv.org/abs/2503.09950 · HTML: https://mlsanity.com/paper/2503.09950/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 70 of its 89 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 70)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation](https://mlsanity.com/paper/2305.16213/) (2023)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [Improved Distribution Matching Distillation for Fast Image Synthesis](https://mlsanity.com/paper/2405.14867/) (2024)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)

## Built on by (most cited first, 30 of 31)

- [STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation](https://mlsanity.com/paper/2505.18647/) (2025)
- [TrajFlow: Multi-modal Motion Prediction via Flow Matching](https://mlsanity.com/paper/2506.08541/) (2025)
- [EgoTraj-Bench: Towards Robust Trajectory Prediction Under Ego-view Noisy Observations](https://mlsanity.com/paper/2510.00405/) (2025)
- [TrajEvo: Designing Trajectory Prediction Heuristics via LLM-driven Evolution](https://mlsanity.com/paper/2505.04480/) (2025)
- [TrajEvo: Trajectory Prediction Heuristics Design via LLM-driven Evolution](https://mlsanity.com/paper/2508.05616/) (2025)
- [JointDiff: Bridging Continuous and Discrete in Multi-Agent Trajectory Generation](https://mlsanity.com/paper/2509.22522/) (2025)
- [FlowDrive: Energy Flow Field for End-to-End Autonomous Driving](https://mlsanity.com/paper/2509.14303/) (2025)
- [From Flow to One Step: Real-Time Multi-Modal Trajectory Policies via Implicit Maximum Likelihood Estimation-based Distribution Distillation](https://mlsanity.com/paper/2603.09415/) (2026)
- [Large Foundation Models for Trajectory Prediction in Autonomous Driving: A Comprehensive Survey](https://mlsanity.com/paper/2509.10570/) (2025)
- [CRFT: Consistent-Recurrent Feature Flow Transformer for Cross-Modal Image Registration](https://mlsanity.com/paper/2604.05689/) (2026)
- [Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2605.10717/) (2026)
- [Recent Advances in Multi-Agent Human Trajectory Prediction: A Comprehensive Review](https://mlsanity.com/paper/2506.14831/) (2025)
- [AGMA: Adaptive Gaussian Mixture Anchors for Prior-Guided Multimodal Human Trajectory Forecasting](https://mlsanity.com/paper/2602.04204/) (2026)
- [DD-MDN: Human Trajectory Forecasting with Diffusion-Based Dual Mixture Density Networks and Uncertainty Self-Calibration](https://mlsanity.com/paper/2602.11214/) (2026)
- [Social-Mamba: Socially-Aware Trajectory Forecasting with State-Space Models](https://mlsanity.com/paper/2605.15424/) (2026)
- [PatchTraj: Unified Time-Frequency Representation Learning via Dynamic Patches for Trajectory Prediction](https://mlsanity.com/paper/2507.19119/) (2025)
- [Coherent Multi-Agent Trajectory Forecasting in Team Sports with CausalTraj](https://mlsanity.com/paper/2511.18248/) (2025)
- [SLD-L2S: Hierarchical Subspace Latent Diffusion for High-Fidelity Lip to Speech Synthesis](https://mlsanity.com/paper/2602.11477/) (2026)
- [Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation](https://mlsanity.com/paper/2604.05303/) (2026)
- [JACoP: Joint Alignment for Compliant Multi-Agent Prediction](https://mlsanity.com/paper/2605.11385/) (2026)
- [CrossVLA: Cross-Paradigm Post-Training and Inference Optimization for Vision-Language-Action Models](https://mlsanity.com/paper/2605.21854/) (2026)
- [Diverse Yet Consistent: Context-Guided Diffusion with Energy-Based Joint Refinement for Multi-Agent Motion Prediction](https://mlsanity.com/paper/2605.22017/) (2026)
- [Sparse Compositional Flow Matching by geometric assembly from motion primitives](https://mlsanity.com/paper/2605.23341/) (2026)
- [Agent-Centric Social Trajectory Prediction: A Free Energy Principle Perspective](https://mlsanity.com/paper/2605.25748/) (2026)
- [MUSCLE-NET: Predicted-Multiscale-Aware Network for Pedestrian Trajectory Forecasting](https://mlsanity.com/paper/2606.00471/) (2026)
- [TrajRS: Towards Certified Robustness in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2606.28716/) (2026)
- [ACME: A Multi-Cultural, Multi-Embodiment Social-Navigation Dataset](https://mlsanity.com/paper/2607.21964/) (2026)
- [A Unified Framework for Trajectory Prediction with Explicit Planning and Reaction Decomposition](https://mlsanity.com/paper/2608.05673/) (2026)
- [CrowdTraj: A Benchmark for Dense Crowd Trajectory Prediction in Realistic Crowded Environments](https://mlsanity.com/paper/2609.07685/) (2026)
- [MedPCFM-TED: One-Step Point Cloud Flow Matching for Implant Generation via Teacher-Guided Endpoint Distillation](https://mlsanity.com/paper/2609.16934/) (2026)

## Abstract (arXiv)

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io