P3: Persistent Particle Planning for Constrained Diffusion Control

Hikmet Simsir; Mahyar Fardinfar; Ozgur S. Oguz

cs.ROOct 5, 2026

P3: Persistent Particle Planning for Constrained Diffusion Control

Authors: Hikmet Simsir, Mahyar Fardinfar, Ozgur S. Oguz

Organizations: Department of Computer Engineering, Bilkent University

Abstract

Diffusion models provide expressive priors over trajectories, but adapting these priors to test-time constraints requires maintaining feasibility and consistency across successive control decisions. We introduce Persistent Particle Planning (P3), a sequential Monte Carlo framework for diffusion control that maintains a weighted population of candidate plans across replanning steps. At each control step, P3 shifts and partially re-noises the candidate trajectories, refines them under the latest observation, and uses constraint-aware weighting and resampling to select among alternative continuations without retraining the diffusion model. We consider denoising and replanning as one Feynman--Kac particle system and analyze it under an idealized repair. We prove that the re-noising depth controls how reliably a kept plan stays on its route, and that keeping a rare, well-separated route takes far fewer plans than rediscovering it by sampling from scratch. Experiments under multiple test-time constraint configurations show that population reuse reduces route switching and improves success without constraint violations. Because P3 refines earlier plans instead of redrawing them, it also needs fewer denoising iterations per replan. On maze-navigation tasks, it plans faster than both regenerated populations and methods that correct a single sampled plan by constrained optimization. Code and pretrained models are available at https://github.com/p3-username/p3-anon.

Figures & tables

Figure 1: Persistent particle planning. Within each planning call (denoising clock, vertical), particles are denoised, weighted by their constraint violation and resampled. After the selected plan’s first action is executed (control clock, horizontal), the population is shifted and re-noised to

t_{0}

rather than redrawn from noise. Bottom: the corresponding plans around an obstacle and a test-time exclusion region.

Figure 2: (a) Clean success on the cluttered configuration of Section 4 , with one or

16

plans, redrawn or kept (Table 9 ). (b) Side switches after one learned repair, relative to a fresh draw, at ten fixed Avoiding states where fresh plans end on both sides of the centerline; black: the three states whose two routes are well separated.

Figure 3: Tasks and test-time constraints. Left: D3IL Avoiding with its four added configurations; the dotted line is the centerline of the plan-side switch metric. Right: the large PointMaze with its broad and narrow presets (top), the medium PointMaze with our blocked preset, whose only clean route is the detour, and AntMaze U with an exclusion disc at the turn (bottom). None of the added constraints appears in the training data.

	Avoiding				Large maze		Medium	AntMaze
Method	Both	Clutt.	Left	Right	Broad	Narrow	Blocked	Turn
Unguided	$0.00\,{\scriptstyle\pm\,0.01}$	$0.00\,{\scriptstyle\pm\,0.00}$	$0.09\,{\scriptstyle\pm\,0.07}$	$0.05\,{\scriptstyle\pm\,0.08}$	$0.06\,{\scriptstyle\pm\,0.10}$	$0.02\,{\scriptstyle\pm\,0.05}$	$0.00\,{\scriptstyle\pm\,0.00}$	$0.38\,{\scriptstyle\pm\,0.11}$
RDM + projection	$0.60\,{\scriptstyle\pm\,0.11}$	$0.09\,{\scriptstyle\pm\,0.05}$	$0.60\,{\scriptstyle\pm\,0.10}$	$0.36\,{\scriptstyle\pm\,0.14}$	$0.50\,{\scriptstyle\pm\,0.11}$	$0.72\,{\scriptstyle\pm\,0.10}$	$\mathbf{0.24}\,{\scriptstyle\pm\,0.09}$	$0.37\,{\scriptstyle\pm\,0.15}$
Projection	$0.85\,{\scriptstyle\pm\,0.05}$	$0.46\,{\scriptstyle\pm\,0.26}$	$0.83\,{\scriptstyle\pm\,0.05}$	$0.79\,{\scriptstyle\pm\,0.10}$	$0.66\,{\scriptstyle\pm\,0.22}$	$0.91\,{\scriptstyle\pm\,0.15}$	$0.11\,{\scriptstyle\pm\,0.09}$	$0.40\,{\scriptstyle\pm\,0.04}$
DiRecT	$0.92\,{\scriptstyle\pm\,0.06}$	$0.28\,{\scriptstyle\pm\,0.12}$	$0.84\,{\scriptstyle\pm\,0.03}$	$0.88\,{\scriptstyle\pm\,0.10}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$\mathbf{0.98}\,{\scriptstyle\pm\,0.04}$	$0.12\,{\scriptstyle\pm\,0.11}$	$0.48\,{\scriptstyle\pm\,0.09}$
SafeDiffuser	$0.44\,{\scriptstyle\pm\,0.17}$	$0.16\,{\scriptstyle\pm\,0.12}$	$0.66\,{\scriptstyle\pm\,0.31}$	$0.34\,{\scriptstyle\pm\,0.30}$	$0.30\,{\scriptstyle\pm\,0.36}$	$0.04\,{\scriptstyle\pm\,0.08}$	$0.00\,{\scriptstyle\pm\,0.01}$	$0.39\,{\scriptstyle\pm\,0.14}$

Table 1: Clean success under test-time constraints, mean

\pm

standard deviation across five model seeds (AntMaze: six evaluation seeds). Avoiding columns: both-hard, cluttered, left-hard, right-hard. Upper rows plan one sample per step, lower rows a population. Trial counts and settings: Appendix C ; additional metrics: Appendix D .

Figure 4: Ablations on cluttered, mean

\pm

one standard deviation over five model seeds. (a) Clean success against the population size. (b) Plan-side switches and (c) clean success with carried or reset weights against the re-noising depth

t_{0}

, at

N=16

. Dashed: SMC. Details: Appendix E .

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Learned repair at fixed states. (a) Correlation along held-out plan directions against the exact-repair floor derived in Appendix A.3 . (b) Side-fraction drift at the ten decision states; (E) predicts zero. Black: the three states whose two routes are well separated.

		clean		cold SMC		P3, all steps		P3, $\nu_{k}<1/N$
Task	Seed	cold	P3	lost all	$\nu_{k}$ there	$\hat{q}_{k}^{\mathrm{desc}}$	$\hat{r}^{\mathrm{rep}}_{k}$	held	fresh
Cluttered	1	0/10	10/10	10/10	0.016	1.00	0.95	0.82	0.13
Cluttered	2	0/10	9/10	10/10	0.016	1.00	0.94	0.61	0.22
Cluttered	3	8/10	9/10	7/10	0.031	1.00	0.96	0.54	0.17
Narrow maze	1	0/5	2/5	5/5	0.000	1.00	1.00	0.27	0.05
Narrow maze	2	0/5	4/5	5/5	0.000	1.00	1.00	0.30	0.07

Appendix

Table 2: Find/keep diagnostics. Lost all: cold-SMC episodes with no acceptable plan at some step;

\nu_{k}

there: median estimated fresh rate at such lapses. Retention columns report medians. Held: fraction of P3 steps with an acceptable plan among states with estimated

\nu_{k}<1/N

; fresh: mean plug-in estimate

1-(1-\nu_{k})^{N}

at those same states.

	Avoiding				Large maze		Medium	AntMaze
Method	Both	Cluttered	Left	Right	Broad	Narrow	Blocked	Turn
Task success $\uparrow$
Unguided	$0.80\,{\scriptstyle\pm\,0.11}$	$0.79\,{\scriptstyle\pm\,0.11}$	$0.80\,{\scriptstyle\pm\,0.11}$	$0.79\,{\scriptstyle\pm\,0.11}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$\mathbf{0.76}\,{\scriptstyle\pm\,0.17}$	$0.82\,{\scriptstyle\pm\,0.08}$
RDM + projection	$0.77\,{\scriptstyle\pm\,0.10}$	$0.85\,{\scriptstyle\pm\,0.05}$	$0.79\,{\scriptstyle\pm\,0.10}$	$0.63\,{\scriptstyle\pm\,0.10}$	$0.88\,{\scriptstyle\pm\,0.12}$	$0.98\,{\scriptstyle\pm\,0.04}$	$0.58\,{\scriptstyle\pm\,0.10}$	$0.84\,{\scriptstyle\pm\,0.06}$
Projection	$0.87\,{\scriptstyle\pm\,0.05}$	$0.97\,{\scriptstyle\pm\,0.02}$	$0.95\,{\scriptstyle\pm\,0.02}$	$0.88\,{\scriptstyle\pm\,0.08}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$0.26\,{\scriptstyle\pm\,0.13}$	$0.83\,{\scriptstyle\pm\,0.08}$
DiRecT	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$0.72\,{\scriptstyle\pm\,0.12}$	$0.88\,{\scriptstyle\pm\,0.03}$	$0.93\,{\scriptstyle\pm\,0.07}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$\mathbf{1.00}\,{\scriptstyle\pm\,0.00}$	$0.12\,{\scriptstyle\pm\,0.11}$	$0.85\,{\scriptstyle\pm\,0.09}$

Appendix

Table 3: Task success for the runs in Table 1 , irrespective of constraint violations. Means and standard deviations are across model seeds (evaluation seeds on AntMaze); trial counts are as in Table 4 .

Accumulated violation $\downarrow$
	Avoiding
Method	Both-hard	Cluttered	Left-hard	Right-hard
Unguided	$2.717\,{\scriptstyle\pm\,0.788}$	$2.463\,{\scriptstyle\pm\,0.582}$	$1.484\,{\scriptstyle\pm\,2.506}$	$6.992\,{\scriptstyle\pm\,3.522}$
RDM + projection	$0.295\,{\scriptstyle\pm\,0.086}$	$0.594\,{\scriptstyle\pm\,0.274}$	$0.646\,{\scriptstyle\pm\,0.361}$	$1.030\,{\scriptstyle\pm\,0.987}$
Projection	$0.035\,{\scriptstyle\pm\,0.040}$	$0.016\,{\scriptstyle\pm\,0.015}$	$0.025\,{\scriptstyle\pm\,0.019}$	$0.215\,{\scriptstyle\pm\,0.188}$
DiRecT	$\mathbf{0.000}\,{\scriptstyle\pm\,0.000}$	$0.021\,{\scriptstyle\pm\,0.014}$	$0.004\,{\scriptstyle\pm\,0.001}$	$0.003\,{\scriptstyle\pm\,0.004}$

Appendix

Table 4: Accumulated violation, mean

\pm

standard deviation across five model seeds (clean success is in Table 1 ). Avoiding:

50

trials per seed (

100

for the population rows); best-of-

N

, SMC and P3 use

N=32

and margin

0.04

, P3 with eight fresh particles per step (Section 4.1 ); the last Avoiding block is P3 at the same setting without rejuvenation. Mazes: large maze (

H=64

), medium maze (

H=8

) and AntMaze U (

H=32

50

trials per seed (AntMaze: six evaluation seeds of

20

paired trials; large-maze Projection:

5

–

10

); population methods use

N=16

, except on AntMaze (

N=4

). Unguided, RDM + projection and Projection use one sample; persistent best-of-

N

uses P3’s setting without weighting or resampling (Appendix E.4 ); RDM + projection uses

10

trials per seed on the large maze (Appendix B ).

	Plan switches $\downarrow$		Episode length (steps) $\downarrow$
Method	Broad	Narrow	Broad	Narrow
Unguided	$72.6\,{\scriptstyle\pm\,15.9}$	$72.5\,{\scriptstyle\pm\,15.9}$	$\mathbf{529}\,{\scriptstyle\pm\,39}$	$528\,{\scriptstyle\pm\,38}$
Projection	$58.6\,{\scriptstyle\pm\,17.2}$	$37.8\,{\scriptstyle\pm\,10.5}$	$535\,{\scriptstyle\pm\,36}$	$432\,{\scriptstyle\pm\,60}$
Best-of- $N$	$68.3\,{\scriptstyle\pm\,18.6}$	$44.9\,{\scriptstyle\pm\,11.0}$	$586\,{\scriptstyle\pm\,39}$	$426\,{\scriptstyle\pm\,5}$
SMC	$69.1\,{\scriptstyle\pm\,21.8}$	$43.2\,{\scriptstyle\pm\,13.8}$	$615\,{\scriptstyle\pm\,50}$	$421\,{\scriptstyle\pm\,16}$
P3 (ours)	$\mathbf{44.5}\,{\scriptstyle\pm\,11.7}$	$\mathbf{28.2}\,{\scriptstyle\pm\,4.8}$	$620\,{\scriptstyle\pm\,84}$	$\mathbf{408}\,{\scriptstyle\pm\,6}$

Appendix

Table 5: Large maze: plan switches (changes of the selected plan’s end cell) per episode and episode length for the runs of Table 4 , mean

\pm

standard deviation across five model seeds.

	Projection		P3
Case	Base	$0.04$	Base	$0.04$
Both-hard	$0.834\,{\scriptstyle\pm\,0.063}$	$0.942\,{\scriptstyle\pm\,0.044}$	$0.944\,{\scriptstyle\pm\,0.036}$	$0.986\,{\scriptstyle\pm\,0.015}$
Cluttered	$0.446\,{\scriptstyle\pm\,0.270}$	n/a	$0.980\,{\scriptstyle\pm\,0.009}$	$0.994\,{\scriptstyle\pm\,0.008}$
Left-hard	$0.824\,{\scriptstyle\pm\,0.112}$	$0.364\,{\scriptstyle\pm\,0.240}$	$0.892\,{\scriptstyle\pm\,0.103}$	$0.936\,{\scriptstyle\pm\,0.037}$
Right-hard	$0.796\,{\scriptstyle\pm\,0.095}$	$0.108\,{\scriptstyle\pm\,0.135}$	$0.966\,{\scriptstyle\pm\,0.043}$	$0.978\,{\scriptstyle\pm\,0.044}$

Appendix

Table 6: Avoiding margin sensitivity: clean success, mean

\pm

standard deviation across five model seeds and

100

trials per seed. Base margin is

0.025

, except

0.01

on cluttered. P3 uses

N=32

and eight fresh particles per step throughout.

Figure 6: Executed paths on cluttered (twenty trials per method on the model seed whose Projection clean success is closest to its five-seed mean) and on the medium maze (the 50 trials per method of one model seed, within

0.07

of the five-seed mean clean success for every method). Cluttered uses

N=16

t_{0}=10

, potential margin

0.01

and no rejuvenation, rather than the Table 1 setting; the medium-maze runs use that table’s setting. The plots show side changes around the exclusion regions on cluttered (left) and trajectories through or around the blocked corridor on the medium maze (right).

Constraint configuration	Projection	SMC	P3 (ours)
Plan-side switches per episode $\downarrow$
Both-hard	$5.34\,{\scriptstyle\pm\,2.70}$	$4.49\,{\scriptstyle\pm\,1.56}$	$\mathbf{1.79}\,{\scriptstyle\pm\,0.90}$
Cluttered	$12.42\,{\scriptstyle\pm\,2.56}$	$10.63\,{\scriptstyle\pm\,2.92}$	$\mathbf{7.72}\,{\scriptstyle\pm\,0.91}$
Left-hard	$7.28\,{\scriptstyle\pm\,3.36}$	$2.87\,{\scriptstyle\pm\,1.02}$	$\mathbf{2.35}\,{\scriptstyle\pm\,0.62}$
Right-hard	$11.10\,{\scriptstyle\pm\,4.09}$	$3.31\,{\scriptstyle\pm\,0.95}$	$\mathbf{2.63}\,{\scriptstyle\pm\,0.46}$

Appendix

Table 7: Projection, SMC and P3 on Avoiding at their Table 1 settings. SMC and P3 use

N=32

, margin

0.04

and

100

trials per seed; Projection uses one plan and

50

trials per seed. Entries are means

\pm

standard deviations across five model seeds.

Figure 7: One example episode of SMC and P3 on both-hard and cluttered. These runs use

N=16

t_{0}=10

, potential margin

0.01

and no rejuvenation, with eight episodes per method and configuration. Top: the executed path, with each selected plan’s endpoint coloured by its side of the centerline, so a colour change is a plan-side switch. Bottom: realization error, the distance between each plan’s endpoint and the position reached

H-1

steps later (black), with the 10–90% band of the other seven episodes of the same method and configuration.

	Cluttered		Narrow		Medium maze		AntMaze
Method	Median	Mean	Median	Mean	Median	Mean	Median	Mean
Unguided	121	120	107	108	86	86	213	213
RDM + projection	4.8	41	5.5	6.4	44	51	653	621
Projection	142	149	27 238	26 143	101	101	214	236
DiRecT	100	101	467	688	139	138	399	2 048
SafeDiffuser	235	236	328	331	210	210	493	486

Appendix

Table 8: Wall-clock time per control step in milliseconds, median and mean over the timed steps, on one RTX 4070 Ti. Each method uses its Table 1 setting, except that the AntMaze population rows are timed at

N=32

. P3 rejuvenates only on Avoiding, and the last row times it there without rejuvenation.

	Task succ. $\uparrow$	Clean succ. $\uparrow$	Violation $\downarrow$	Switches $\downarrow$	Evals $\downarrow$	s/step
SMC
$N=1$	$0.75\,{\scriptstyle\pm\,0.11}$	$0.00\,{\scriptstyle\pm\,0.00}$	$2.3805\,{\scriptstyle\pm\,0.5500}$	$7.46\,{\scriptstyle\pm\,3.34}$	20	0.060
$N=2$	$0.62\,{\scriptstyle\pm\,0.07}$	$0.02\,{\scriptstyle\pm\,0.02}$	$0.8752\,{\scriptstyle\pm\,0.2505}$	$11.22\,{\scriptstyle\pm\,4.76}$	40	0.117
$N=4$	$0.77\,{\scriptstyle\pm\,0.18}$	$0.16\,{\scriptstyle\pm\,0.20}$	$0.1440\,{\scriptstyle\pm\,0.1234}$	$12.92\,{\scriptstyle\pm\,4.03}$	80	0.114
$N=8$	$0.87\,{\scriptstyle\pm\,0.10}$	$0.31\,{\scriptstyle\pm\,0.31}$	$0.0445\,{\scriptstyle\pm\,0.0400}$	$12.88\,{\scriptstyle\pm\,4.71}$	160	0.105
$N=16$	$0.90\,{\scriptstyle\pm\,0.08}$	$0.35\,{\scriptstyle\pm\,0.33}$	$0.0323\,{\scriptstyle\pm\,0.0288}$	$11.42\,{\scriptstyle\pm\,5.21}$	320	0.115

Appendix

Table 9: Population size on cluttered constraints, at matched

N

for SMC and P3 (

t_{0}=10

). Violation is the accumulated residual along the executed path and switches are plan-side changes per episode; lower is preferable for both. Evals is

N

times the number of reverse iterations: per planning call for SMC and per warm replanning call for P3. P3’s first call uses the full

20

iterations. s/step is wall-clock measured under the protocol in Appendix C , in a separate run from Table 10 . Denoiser evaluations grow linearly in

N

, whereas measured latency changes little between

N=2

and

N=16

	Task succ. $\uparrow$	Clean succ. $\uparrow$	Violation $\downarrow$	Switches $\downarrow$	Iter.	s/step
SMC	$0.90\,{\scriptstyle\pm\,0.08}$	$0.35\,{\scriptstyle\pm\,0.33}$	$0.0323\,{\scriptstyle\pm\,0.0288}$	$11.42\,{\scriptstyle\pm\,5.21}$	20	0.114
$t_{0}=2$	$0.96\,{\scriptstyle\pm\,0.03}$	$0.84\,{\scriptstyle\pm\,0.13}$	$0.1201\,{\scriptstyle\pm\,0.1122}$	$3.18\,{\scriptstyle\pm\,0.56}$	3	0.020
$t_{0}=4$	$0.99\,{\scriptstyle\pm\,0.01}$	$0.98\,{\scriptstyle\pm\,0.02}$	$0.0106\,{\scriptstyle\pm\,0.0211}$	$3.82\,{\scriptstyle\pm\,0.48}$	5	0.031
$t_{0}=6$	$1.00\,{\scriptstyle\pm\,0.00}$	$0.98\,{\scriptstyle\pm\,0.01}$	$0.0001\,{\scriptstyle\pm\,0.0001}$	$3.80\,{\scriptstyle\pm\,0.41}$	7	0.043
$t_{0}=8$	$1.00\,{\scriptstyle\pm\,0.00}$	$0.99\,{\scriptstyle\pm\,0.01}$	$0.0000\,{\scriptstyle\pm\,0.0000}$	$4.12\,{\scriptstyle\pm\,0.57}$	9	0.053
$t_{0}=10$	$1.00\,{\scriptstyle\pm\,0.01}$	$0.99\,{\scriptstyle\pm\,0.02}$	$0.0035\,{\scriptstyle\pm\,0.0070}$	$4.46\,{\scriptstyle\pm\,0.59}$	11	0.063

Appendix

Table 10: Re-noising depth on cluttered constraints at

N=16

with carried weights. The SMC row is the cold-start control.

t_{0}=19=K-1

re-noises to the start of the reverse chain. The accumulated weights are retained, but the re-noised input depends only weakly on the previous trajectory. Iter. counts reverse diffusion iterations per warm replanning call for P3 and per planning call for SMC; P3’s first call uses all

20

iterations. Latency uses the separate serial CPU protocol of Appendix C . Cold SMC and

t_{0}=19

have the same number of denoising iterations and latencies within

1\%

	Clean succ. $\uparrow$	Violation $\downarrow$	Switches $\downarrow$
$t_{0}=2$	$0.84\,{\scriptstyle\pm\,0.13}$	$0.2293\,{\scriptstyle\pm\,0.2035}$	$3.56\,{\scriptstyle\pm\,0.61}$
$t_{0}=4$	$0.94\,{\scriptstyle\pm\,0.06}$	$0.0559\,{\scriptstyle\pm\,0.0888}$	$4.04\,{\scriptstyle\pm\,0.27}$
$t_{0}=6$	$0.98\,{\scriptstyle\pm\,0.01}$	$0.0079\,{\scriptstyle\pm\,0.0158}$	$4.12\,{\scriptstyle\pm\,0.31}$
$t_{0}=8$	$0.97\,{\scriptstyle\pm\,0.02}$	$0.0002\,{\scriptstyle\pm\,0.0002}$	$4.58\,{\scriptstyle\pm\,0.48}$
$t_{0}=10$	$0.98\,{\scriptstyle\pm\,0.03}$	$0.0037\,{\scriptstyle\pm\,0.0072}$	$4.76\,{\scriptstyle\pm\,0.62}$
$t_{0}=12$	$0.98\,{\scriptstyle\pm\,0.01}$	$0.0034\,{\scriptstyle\pm\,0.0066}$	$4.90\,{\scriptstyle\pm\,0.52}$

Appendix

Table 11: Resetting weights to uniform at every control step, at

N=16

on cluttered. The carried-weight comparison is in Table 10 . Both variants retain trajectories and differ only in the weights entering the next step.

	Method	Both-hard	Cluttered	Left-hard	Right-hard
Clean	Persistent best-of- $N$	$0.54\,{\scriptstyle\pm\,0.30}$	$0.87\,{\scriptstyle\pm\,0.18}$	$0.46\,{\scriptstyle\pm\,0.12}$	$0.77\,{\scriptstyle\pm\,0.18}$
	P3	$0.78\,{\scriptstyle\pm\,0.13}$	$0.99\,{\scriptstyle\pm\,0.01}$	$0.81\,{\scriptstyle\pm\,0.14}$	$0.95\,{\scriptstyle\pm\,0.05}$
Violation	Persistent best-of- $N$	$0.6503\,{\scriptstyle\pm\,0.8046}$	$0.0009\,{\scriptstyle\pm\,0.0012}$	$0.0245\,{\scriptstyle\pm\,0.0113}$	$0.0128\,{\scriptstyle\pm\,0.0216}$
	P3	$0.2855\,{\scriptstyle\pm\,0.3524}$	$0.0045\,{\scriptstyle\pm\,0.0088}$	$0.0065\,{\scriptstyle\pm\,0.0059}$	$0.0004\,{\scriptstyle\pm\,0.0005}$
Switches	Persistent best-of- $N$	$1.48\,{\scriptstyle\pm\,0.53}$	$4.80\,{\scriptstyle\pm\,0.70}$	$3.55\,{\scriptstyle\pm\,1.41}$	$4.54\,{\scriptstyle\pm\,1.12}$
	P3	$1.39\,{\scriptstyle\pm\,0.44}$	$4.44\,{\scriptstyle\pm\,0.54}$	$3.68\,{\scriptstyle\pm\,1.03}$	$4.45\,{\scriptstyle\pm\,0.59}$

Appendix

Table 12: Persistent best-of-

N

against P3 at the ablation setting (

N=16

t_{0}=10

, margin

0.01

, no rejuvenation), five model seeds with 100 trials each.

Figure 8: Executed paths on the large maze for one model seed, broad (top) and narrow (bottom). Blue: goal reached cleanly; orange: after a violation. Titles give clean success, mean penetration and trial count

n

Figure 9: Medium maze, blocked. Left: the

200

training demonstrations, half through the detour (red) and half through the direct corridor (blue); the obstacles exist only at test time. Right: the unguided

H=8

model takes the direct corridor on every trial in the plotted seed (orange: goal after a violation; grey: failure).

$N$	SMC	P3 (ours)
4	$0.53\,{\scriptstyle\pm\,0.11}$	$0.62\,{\scriptstyle\pm\,0.10}$
8	$0.50\,{\scriptstyle\pm\,0.12}$	$0.57\,{\scriptstyle\pm\,0.12}$
16	$0.58\,{\scriptstyle\pm\,0.09}$	$0.57\,{\scriptstyle\pm\,0.10}$
32	$0.60\,{\scriptstyle\pm\,0.08}$	$0.61\,{\scriptstyle\pm\,0.10}$

Appendix

Table 13: AntMaze clean success of SMC and P3 by population size

N

, mean

\pm

standard deviation across six evaluation seeds of

20

trials. Table 1 reports

N=4

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May 16, 2026cs.RO

Plan First, Diffuse Later: Extrinsic Graph Guidance for Long-Horizon Diffusion Planning

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/

Yaniv Hassidof, Adir Morgan, Yilun Du +1

Technion · Harvard

Diffusion Planning Long-Horizon Planning Diffusion Models Single Trajectory Motion Coherence

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