The lottery, drawn twice
A robot's correct action is often a set, not a point. Representing that set is what an energy landscape does for free and what a regression policy structurally cannot do. The question this instrument answers is not which is smarter. It is what each one costs on the substrate underneath it, and the answer changes depending on which substrate you are standing on.
Predict first
A robot can go around an obstacle to the left or to the right. Both routes appear in the human demonstrations, equally often. The policy is trained by minimising mean squared error against those demonstrations. At run time, what does it do?
The task
One way is a unique answer. Two or more is a set, and the set is what a squared-error loss cannot hold.
Substrate A: von Neumann
Diffusion Policy samples its action by running Langevin steps on a learned gradient
field. Each step is one network forward pass, and the steps are serial. Published range is
10–100 NFE per action.
The steps are buying accuracy, and width cannot buy it instead. Measured
against an exact optimum: on a fully actuated plant, at a single pass, one joint reaches
0.57% of optimal and eight joints reach only 78.74%, about
138 times worse, and no noise setting recovers it. The direction holds on every plant
tested, including an underactuated one; the size of the effect is largest when every joint is
driven. Refinement passes close the gap at every dimension, and the number of passes needed
grows with the joint count. That is why this slider costs what it costs, and why it costs more
on a bigger body.
Substrate B: a fabric that settles
The fabric holds the landscape and relaxes into it. Cost does not grow with the number of modes or the number of steps, because there are no steps. What it costs instead is imposing the new state each tick. 100 ms is a measured figure, not an assumption.
The body
A scalar toy and a seven-jointed arm are different problems. The accuracy below is measured at the nearest dimension actually swept (1, 2, 4, 8), with the exploration noise scaled so total perturbation is constant, which is what makes the dimensions comparable.
On a body
Measured on a three-joint arm with gravity, actuator lag, torque limits and an
identified power model, against an analytic reference controller that reaches every target at
26.4 J. At a matched compute budget, spending it on refinement rather than
width is the difference between reaching 9 of 24 targets and 24 of 24. With enough
refinement the sampler reaches every target at 17.8 J, 33% less actuation than
the reference. And the floor shows up here too: at one pass, 200 rollouts and 800 rollouts
both reach 9 of 24.
And pricing joules inside the objective does not help. Putting the same
power model into the controller's cost made the delivered figure worse, from
17.4 to 19.7 J per completed task, because the controller grows
reluctant on hard targets and a standing 9 W draw charges the extra seconds back.
The median hides it entirely: read that column and it looks like a 4% improvement.
The deadline
Visuomotor policies commonly run near 10 Hz with action chunking, and the pressure is upward. Every rung here is reachable by some setting of the two substrate controls, so if a rung is failing, it is failing for a reason you can go and change.
Where these numbers come from
| Quantity | Value | Status |
|---|---|---|
| Denoising steps per action | 10–100 NFE | published range |
| Network forward pass | 3 ms | stated assumption |
| Embedded Ising machine, end to end | ~100 ms | measured |
| Ising fabric size | 2,048 spins | measured |
| Coupling-matrix compression | 32x | measured |
Diffusion Policy, arXiv:2303.04137 and its literature, which names the
10–100 NFE cost as the key barrier to real-time deployment. The 100 ms is Toshiba's
measured system-wide latency, independent of problem size, on an FPGA simulated-bifurcation
machine (arXiv:2503.23966). The 3 ms forward pass is an assumption of this instrument and the quantity a reader is most
likely to have better information about. Change it and the crossing point moves proportionally.