The mechanism
A diffusion action policy generates a sequence of future commands conditioned on observations. Receding-horizon execution applies only a prefix, then receives new observations and generates another sequence. The prediction horizon and action-execution horizon are therefore different parameters. Executing a longer prefix reduces replanning frequency but delays reactions to disturbances. Inference latency also consumes part of the control budget and must be measured or explicitly assumed. Diffusion Policy studies this structure; the scalar command sequence here is a worked control trace, not a trained denoising policy.
- Record the observation time and generate an action chunk under a declared policy identity.
- Execute only the selected prefix with an explicit command/period convention.
- Observe disturbances and update the next planning state.
- Compare closed-loop and open-loop outcomes while separating assumed inference delay from actual transition arithmetic.
Science and assumptions
Predict action chunks and replan with feedback · worked relation
Separate generated action horizon, executed prefix and replanning interval.
Symbols and units
- T_prefix
- Time covered by executed action prefix
s
- H_a
- Executed commands before replanning
commands
- f
- Command rate
commands per s
- x_t
- Position
m
- a_t
- Position increment command
m per step
- d_t
- Disturbance at the declared step
m
For , start x=0 and an authored chunk [1,1,1,1] targeting x=4. After executing the first command, a disturbance adds +1, so observed x=2. Replanning with [1,1,0,0] and executing the next two commands reaches 4. Executing all three remaining original commands instead reaches 5. At an assumed 10 Hz command rate, a two-command prefix covers 0.2 s; an assumed 0.05 s inference delay is one quarter of that interval, not a measured policy latency.
Assumptions Authored deterministic scalar integrator and command chunks. Rate and delay are stated assumptions; no diffusion inference or physical robot timing is measured.
Engineering example
For , start x=0 and an authored chunk [1,1,1,1] targeting x=4. After executing the first command, a disturbance adds +1, so observed x=2. Replanning with [1,1,0,0] and executing the next two commands reaches 4. Executing all three remaining original commands instead reaches 5. At an assumed 10 Hz command rate, a two-command prefix covers 0.2 s; an assumed 0.05 s inference delay is one quarter of that interval, not a measured policy latency.
Distinctions and tradeoffs
It is a mistake to conclude: The original chunk becomes guaranteed correct.
Frequent replanning improves responsiveness but spends more inference work. Long prefixes tolerate delay while increasing open-loop exposure to model and environment error.
Distinguish predicting observations, choosing actions and controlling a changing environment. Separate generated action horizon, executed prefix and replanning interval.
Specifications and interfaces
- Learning mode
- worked example
The executable decoder has 423 parameters; worked extensions do not imply an additional simulator.
- Worked contract
- Separate generated action horizon, executed prefix and replanning interval.
Authored deterministic scalar integrator and command chunks. Rate and delay are stated assumptions; no diffusion inference or physical robot timing is measured.
Interfaces
- Inputs and state Input
- Record the observation time and generate an action chunk under a declared policy identity.
- Result and check Output
- Separate generated action horizon, executed prefix and replanning interval.
Check your understanding
What changes when only a prefix is executed before observing again?
- The next commands can be replanned from the disturbed state.
- The original chunk becomes guaranteed correct.
- The policy’s weights must be retrained after every command.
Answer and reasoning
The next commands can be replanned from the disturbed state.
The next commands can be replanned from the disturbed state. Authored deterministic scalar integrator and command chunks. Rate and delay are stated assumptions; no diffusion inference or physical robot timing is measured.
Evidence and scope
Mode: worked example. Authored deterministic scalar integrator and command chunks. Rate and delay are stated assumptions; no diffusion inference or physical robot timing is measured. Numerical examples are authored calculations, except explicitly identified automated core fixtures. Primary sources support the scoped mechanism; no human specialist review or learner outcome is implied.
Model lifecycle studio: worked example. Authored deterministic scalar integrator and command chunks. Rate and delay are stated assumptions; no diffusion inference or physical robot timing is measured.