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Model-based Diffusion for Trajectory Optimization
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Proposes Model-Based Diffusion (MBD), which uses a known dynamics model and cost to estimate the score function for trajectory optimization without training data, optionally steered by imperfect demonstrations.
Problem
Trajectory optimization with nonlinear, non-smooth dynamics and non-convex costs/constraints; existing diffusion planners are model-free and need high-quality demonstration data, limiting generalization to new robots/dynamics and imperfect data.
Approach
Replace the learned score with a Monte Carlo score estimate computed from model evaluations (rollouts of control sequences through the dynamics, weighted by exp(-cost/lambda) and constraint indicators), run as Monte Carlo score ascent in a diffusion schedule; demonstrations are incorporated via a max-weight target that trusts demos only when model likelihood is low. Connects to CEM when N=1.
Key results
- On Brax locomotion and PushT, MBD achieved the highest reward on all seven tasks (e.g., Half Cheetah 2.31 vs. RL 1.59; Humanoid Running 2.92 vs. RL 1.80) while taking about one-tenth of RL's computation time.
- The paper claims MBD outperforms PPO by 59% across tasks within tens of seconds of diffusing.
- MBD reached 85.5% accuracy on MNIST MLP training with 256 samples in 2 s without gradients, versus 92.7% for SGD with momentum.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MBD instead of RL | Hopper · Hopper | reward: 1.40 ± 0.04 -> 1.53 ± 0.03 | Helped |
| Use MBD instead of RL | Half Cheetah · Half Cheetah | reward: 1.59 ± 0.05 -> 2.31 ± 0.19 | Helped |
| Use MBD instead of RL | Ant · Ant | reward: 3.26 ± 1.61 -> 3.80 ± 0.35 | Helped |
| Use MBD instead of RL | Walker2D · Walker2D | reward: 1.09 ± 0.28 -> 2.63 ± 0.23 | Helped |
| Use MBD instead of RL | Humanoid Standup · Humanoid Standup | reward: 0.83 ± 0.02 -> 0.99 ± 0.07 | Helped |
| Use MBD instead of RL | Humanoid Running · Humanoid Running | reward: 1.80 ± 0.03 -> 2.92 ± 0.26 | Helped |
| Use MBD instead of RL | Push T · Push T | reward: -0.63 ± 0.16 -> 0.67 ± 0.10 | Helped |
| Add infeasible RRT demonstrations from simplified dynamics | MBD · Car UMaze Navigation | goal-reaching performance | Helped |
| Add partial-state CMU Mocap human-motion data | MBD · Humanoid Jogging | motion stability | Helped |
Surprising findings
- With N=1 the method reduces to the Cross-Entropy Method, linking diffusion schedules to sampling-based optimization.
Limitations
- Open-loop control sequences only; compared against closed-loop RL policies
- Shooting-based feasibility can be inefficient for long-horizon tasks with many constraints
- Convergence theory provided only for small-temperature limit under mild assumptions; not fully analyzed
Experimental setup
Datasets: CMU Mocap (humanoid jogging partial-state reference) RRT-generated infeasible trajectories (Car UMaze) MNIST
Benchmarks: Brax locomotion (Hopper, Half Cheetah, Ant, Walker2D, Humanoid Standup, Humanoid Running) PushT Car UMaze navigation Ackley Rastrigin MNIST MLP training
Metrics: average step reward computational time
Baselines: CMA-ES CEM MPPI PPO SAC TuRBO LA-MCTS HesBO Shiwa BAxUS
Builds on: denoising diffusion probabilistic models Cross-Entropy Method Model Predictive Path Integral shooting methods
Closest papers by meaning
- Multi-Robot Motion Planning with Diffusion Models (ICLR 2025 · similarity 0.92)
- One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillation (ICML 2025 · similarity 0.89)
- Score Regularized Policy Optimization through Diffusion Behavior (ICLR 2024 · similarity 0.89)
- Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous and Instruction-guided Driving (CVPR 2024 · similarity 0.89)
- Diffusion Policy Policy Optimization (ICLR 2025 · similarity 0.89)
- Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization (NeurIPS 2024 · similarity 0.88)
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