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Natura non facit saltus.
Nature does not make jumps. — G. W. Leibniz, 1704
Video
§ 01 — Idea
A direct-action policy predicts each chunk of actions on its own, so the motion jumps where chunks meet. ODE policy learns how the action changes and integrates it over the robot's physical time, so each action follows from the previous one.
§ 02 — Results
Ratios against flow matching in imitation learning. Hover over any chart for its numbers.
As a visuomotor policy, as the action head of a VLA and a world action model, and as the actor in RL, ODE policy learns faster than direct-action policies.
Imitation learning on LIBERO
Gain over FM-DiT, less data and smaller models
Action head of a VLA (π0.5)
Action head of a world action model (ImageWAM)
Actor of SuperMimic in reinforcement learning
Gain in training return
Gain in evaluation return
Tasks on four robots, from precise insertion to bimanual and walking manipulation. ODE policy has the highest success rate on all fourteen real-robot tasks, including the three cross-lab tasks under Generalizes. Each card compares it with the best baseline over 20 trials.
Franka Research 3, 40 demonstrations per task, 50 epochs
Put a mango into a box and close the lid.
Grasp a key and hang it on a hook.
Fold a sock, put it into a drawer, close the drawer.
Insert a block into a matching hole.
Galaxea R1 Lite, joint actions, 300 epochs
Insert a thin stem into a narrow opening.
Bowl into the microwave, push it in, close the door. 34 demonstrations.
Insert two flowers one after the other, at least one inserted.
One arm puts an apple into the drawer, the other closes it. Both modes used.
Sharpa North
Pick up a can and place it on a plate. 50 demonstrations.
Unitree G1, action head of GR00T N1.7, 90 demonstrations per task
Walk to a toy, squat to grasp it, and put it into a box on the sofa.
Grasp a rice ball, walk to the microwave, put it inside, close the door.
Where flow matching and diffusion policies fail, ODE policy finishes the task. Click a baseline to see how it fails.
Grasp a bowl, place it in the microwave, push it in, close the door with the other arm.
75% ODE · 20% FM-DiT · 0% DDPM · 0% DDIM
Click a baseline to play it in the large view.
Insert a thin stem into a small opening, which leaves almost no room for error.
30% / 60% ODE · 20% / 40% FM-DiT · 0% / 0% DDPM · 0% / 5% DDIM (poppy / dahlia)
Click a baseline to play it in the large view.
Inference and smoothness on the real robots
Speed and success on LIBERO
At scale, in π0.5
On real dexterous hands, ODE policy transfers skills learned only from public demonstrations of another lab (SharpaDex) to our lab, with other objects and backgrounds and without any demonstration from our setup.
Set a fallen cup upright, with other cups and another background.
SharpaDex data
Our labPour pills between two cups with two hands, with cups of other colors.
SharpaDex data
Our labStack a red cube on a green one, where the demonstrations use wooden cubes.
SharpaDex data
Our labIn simulation, zero-shot on LIBERO-plus, with unseen camera views, initial states, layouts, backgrounds, lighting, and sensor noise.
Visuomotor policies
VLA (π0.5)
WAM (ImageWAM)
A sampled direction tilts the field toward one mode, so ODE policy keeps distinct behaviors. On the real robot, either arm may put the apple into the drawer while the other closes it, and ODE policy uses both.
Learned from 25 demonstrations per mode. Over 20 trials, ODE policy places the apple with the left arm 8 times and with the right arm 12 times, with 5/8 and 7/12 successes (60%). FM-DiT goes for the apple with both arms (14 and 6 times) but succeeds in none.
Rollouts of ODE policy
Task success
Mode balance
§ 03 — Method
ODE policy replaces only the action head. The encoder, the data, and the training schedule stay the same.
The images and the instruction are encoded into an embedding $\mathbf z_t$, as in any policy. The network $\mathbf f_\theta$ outputs how the action should change, given the action $\mathbf a(t)$ the robot is commanded to reach and its proprioception $\mathbf s_t$. Time $t$ is the physical time of the robot.
Because the field sees the current action, each step depends on where the motion has arrived. A direct-action policy outputs a whole chunk at once and cannot react to its own intermediate actions.
Every $H=8$ steps, the policy reads the observation once and holds $\mathbf z_t$ and $\mathbf s_t$ fixed. It then integrates the field with RK4, one action after another, and the next chunk starts from the last integrated action. This gives three benefits.
Chunks join without jumps. The motion is one integral curve whose condition is refreshed every 8 steps.
Each action is sent as soon as it is integrated. A chunk takes 5.7 ms with Euler, against 61 ms for FM-DiT.
The field lives in continuous time, so one model runs at a finer rate by integrating with a smaller step.
Start from a demonstrated action, integrate $H$ steps, and match the whole path. The gradient flows back through the solver, and no velocity labels are needed.
Contractive perturbation. Some segments start from a shifted point $\mathbf a_t+\boldsymbol\delta$, and the target shrinks the shift by $\rho^k$ at step $k$. The field learns to pull drift back, at no cost at inference.
Orange segments are the errors between the integrated steps and their targets. Training removes them.
Paths from perturbed starts return to the demonstration.
A deterministic field averages distinct behaviors, e.g., passing an obstacle on the left or on the right, and heads into the obstacle. A small head reads the features of the field once per chunk and samples a direction $\boldsymbol\epsilon$ with a rate $\boldsymbol\lambda_k$ per step, which tilts the field toward one route. It is trained on detached inputs, so the gradient of $\mathbf f_\theta$ stays unchanged.
In RL, the field acts at every control step ($H=1$) and takes one Euler step from the previous action. Only the actor is replaced, and the RL algorithm trains the field through this step. In SuperMimic, which backpropagates the return through 32 imagined steps of a world model, the identity in $\partial\hat{\mathbf a}_t/\partial\hat{\mathbf a}_{t-1}$ carries the gradient to early actions without decay.
§ 04 — Cite
@article{jia2026ode,
title = {{ODE} Policy: Robot Learning via Action Dynamics, Not Actions},
author = {Jia, Jindou and Li, Jingliang and Zuo, Kuangji and An, Tuo and Hu, Yuxuan and Zhao, Mengfei
and Lyu, Bofan and Bai, Jiaqi and Zhu, Daoyuan and Dai, Hengyu and Zhang, Junpeng and Yang, Jianfei},
journal = {arXiv preprint arXiv:2611.01729},
year = {2026}
}