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The paper's central claim is that embedding search directly inside the diffusion denoising process solves the mode-averaging problem of compositional generative models, allowing short-horizon diffusion models to compose into coherent long-h

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2026-08-03 13:08 UTC pith:DFI3LUJO

load-bearing objection A useful, genuinely combined inference-time sampler for compositional diffusion, but the pruning metric that sets it apart is validated only on a toy and the TAMP version of the method leans on an auxiliary forward-dynamics model that isn't in the main algorithm. the 4 major comments →

arxiv 2601.00126 v3 pith:DFI3LUJO submitted 2025-12-31 cs.RO

Compositional Diffusion with Guided Search for Long-Horizon Planning

Utkarsh A Mishra , David He , Yongxin Chen , Danfei Xu This is my paper
classification cs.RO
keywords compositional diffusionmode averaginglong-horizon planningguided searchDDIM inversioniterative resamplingdiffusion planningtrajectory stitching
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper is trying to establish that the mode-averaging failure of compositional diffusion can be fixed at inference time without retraining, by turning the denoising process itself into a search. The method, CDGS, keeps a population of noisy global plans at each denoising step, resamples overlapping local segments so information from distant parts of the plan propagates end-to-end, and prunes candidates whose local segments fall into low-likelihood regions. The pruning signal is the curvature of each local segment's DDIM-inversion path through the pretrained score network, used as a proxy for local feasibility. If CDGS is right, long-horizon planning, panoramic image synthesis, and long-video generation can all extend far beyond training horizons using only short-horizon models, avoiding the expense of long-horizon data. The paper reports that CDGS matches an oracle planner on seven robot manipulation tasks and improves coherence over plain composition in panoramic images and long videos.

Core claim

CDGS's central claim is that mode averaging arises because naïve score averaging over composed local distributions merges incompatible modes, and that this can be avoided by embedding a guided search in the denoising loop. At every diffusion step the algorithm draws a batch of candidate global plans from the compositional score, applies iterative resampling over overlapping segments so constraints propagate across the chain, ranks candidates by the summed squared time-derivative of the score network along each local segment's DDIM-inversion trajectory, keeps the best K, and repopulates the batch. The paper argues that low-curvature inversion paths indicate high-likelihood local segments, so

What carries the argument

The central object is the CDGS guided-search sampler, built on two interacting parts. Iterative resampling repeatedly re-noises and denoises overlapping variables so that messages propagate along the chain, analogous to belief propagation across factors. The pruning metric is J(τ) = ∏_m exp(-g(y_m)), where g(y) = ∑_i ||∂ ε_θ(y^{(i-1)}, i)/∂i||^2 is the curvature of the DDIM-inversion trajectory of a local segment through the pretrained local score network. This curvature is the paper's proxy for closeness to a mode of the training distribution; pruning by it is what removes mode-averaged, locally infeasible candidates. The mechanism is plug-and-play because it queries only the existing score

Load-bearing premise

The load-bearing premise is that the curvature of a local segment's DDIM-inversion path through the score network reliably ranks whether that segment is locally feasible, so pruning by that curvature removes mode-averaged plans rather than good ones; for the TAMP tasks, the ranking also depends on learned per-skill forward-dynamics models overwriting predicted next states before the metric is applied.

What would settle it

Run CDGS on a suite of long-horizon tasks with known mode sequences and replace the curvature-based ranking with random selection of the same elite fraction at the same batch size; if random selection matches CDGS's success on the seven manipulation tasks, the feasibility signal is not doing the causal work. A cleaner check is to label which mode sequence each candidate plan belongs to and test whether plans retained by J(τ) are the feasible mode sequences more often than chance.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Compositional diffusion can solve long-horizon tasks without long-horizon training data, matching planners that are given an oracle task plan.
  • The same inference-time sampler transfers across domains, producing text-guided panoramas and extending short video clips to hundreds of frames with improved subject consistency.
  • Performance scales with inference compute: larger candidate batches and more resampling steps increase success on harder, longer-horizon tasks, and both resampling and pruning are needed together.
  • The composition stage is training-free; CDGS can wrap an existing pretrained local diffusion score function and improve on plain compositional sampling without modifying the model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The curvature metric and the search structure are separable: a natural extension is to replace the DDIM-curvature proxy with any learned or learned-free feasibility verifier, turning CDGS into a general inference-time search wrapper.
  • Because resampling is belief-propagation-like, one could test how many resampling rounds are needed for goal information to reach the start as the horizon grows, potentially yielding a sharper compute-versus-horizon tradeoff than the linear scaling reported.
  • The TAMP version overwrites predicted next states with learned per-skill forward dynamics before ranking; an ablation that removes that overwrite, or swaps in a dynamics-free verifier, would reveal how much of the reported TAMP success is due to search rather than to the auxiliary dynamics model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes CDGS, an inference-time algorithm that augments compositional diffusion sampling of long-horizon sequences with (i) iterative resampling between overlapping local factors and (ii) population-based pruning of candidate global plans using a DDIM-inversion curvature metric that approximates local likelihood. The method is evaluated on OGBench tasks, a six-task TAMP suite, panoramic image stitching with Stable Diffusion, and long video generation with CogVideoX. The central claim is that CDGS removes the mode-averaging failure of score-averaging composition, producing locally feasible, globally coherent plans without long-horizon training data.

Significance. If the pruning metric is reliable, CDGS is a significant training-free advance for compositional diffusion: it requires only pretrained local score networks, provides adaptive inference-time compute, and is evaluated across robotics, image, and video domains. The paper includes pseudocode, an anonymized code release, external baselines (OGBench, STAP, VBench), and hardware experiments, which are concrete strengths. The significance is conditional on the DDIM-curvature ranking being valid in high-dimensional domains and on the TAMP results reflecting the method as described in the main text; neither is fully established.

major comments (4)
  1. [Sec. 3.1, Eq. (5), Algorithm 1] There is a sign inconsistency in the pruning objective. Eq. (5) defines J as a product of exp(-g(y_m)); a high curvature g (low likelihood) gives a small J. The text then states "Low-quality plans have high J values," and Algorithm 1 selects the K plans minimizing J. Under Eq. (5), minimizing J selects high-curvature (bad) plans. Either the sign in Eq. (5) should be flipped, or the selection should maximize J. Since this is the central pruning mechanism, the inconsistency affects the interpretation of all pruning results.
  2. [Sec. 3.1, Eq. (5), App. D.1] The claim that the DDIM-inversion curvature g(y) ranks local feasibility is validated only on a 1D mixture-of-intervals toy in App. D.1. In TAMP, the local transitions are high-dimensional pose vectors over multiple objects with geometric and symbolic constraints. No experiment shows that curvature correlates with ground-truth transition feasibility in a real domain. Please add a direct evaluation (e.g., correlation of g with ground-truth success, or an ablation replacing the curvature ranking with reconstruction-error or restoration-gap ranking) to support the load-bearing claim.
  3. [Appendix M, Algorithm 3] The TAMP evaluation pipeline is not the algorithm described in the main text. Appendix M states that before computing J, every predicted next state is overwritten with a learned per-skill forward dynamics model f_pi(s_i,a_i), and Algorithm 3 includes this step as line 6. This correction is absent from Algorithm 1 and from the method description in Sec. 3.1. Since Table 2 reports six of the robot tasks, the reported successes may be attributable to this auxiliary correction rather than to the curvature-based pruning. Please add an ablation of CDGS on TAMP without the forward-dynamics overwrite, or incorporate the overwrite into the main method and discuss its necessity.
  4. [Abstract, Sec. 4, Table 2] The abstract's claim that CDGS "matches oracle performance on seven robot manipulation tasks" is not supported by Table 2. On every TAMP task, CDGS is below "GSC (Original) Oracle task plan" (e.g., 0.18 vs 0.48 on Rearrangement Memory Task 2; 0.42 vs 0.82 on Rearrangement Memory Task 1). Even if GSC (Original) uses an oracle task plan and CDGS does not, the wording should be revised to reflect the actual comparison, e.g., "competitive with privileged baselines" or "substantially outperforms LLM/VLM baselines on the most challenging TAMP tasks."
minor comments (4)
  1. [App. F.4.2] The line "Random CEM samples the prior from a uniform distribution? (double-check)" contains an internal query and should be removed or resolved.
  2. [Table 1] The column header "CD" is not defined in the main text; the text refers to CompDiffuser [40], so please use a consistent name and define it in the caption.
  3. [App. L, Eq. (6)] The NFE formula in App. L (T*U + T*T) is inconsistent with the scheduled NFE expression in App. F.2. Please reconcile the two formulas and clarify whether pruning is performed at every step or only in the latter part of denoising.
  4. [Fig. 5 caption] "(H-7) denotes performance averaged over tasks of horizon 7" is confusing typography; please write "H=7".

Circularity Check

0 steps flagged

No circularity found: the pruning metric is an externally validated OOD heuristic, and the TAMP forward-dynamics discrepancy is a validation gap rather than a circular reduction.

full rationale

The paper's derivation chain is not circular at the level of its own equations. The compositional score (Eq. 3) is a standard factor-graph/Bethe score average, and the guided-search claims are checked against external task success (Tables 1-2), panorama metrics (Table 3), and VBench video metrics (Table 4), not against the pruning objective itself. The DDIM-inversion curvature metric (Eq. 5) is an OOD/likelihood heuristic adopted from cited external work [18]; it is not fitted to the target tasks and it is used to rank candidates, while the headline 'matches oracle' claims are grounded in physical task outcomes. Using the same learned score model both to propose plans and to score them is self-referential in an algorithmic sense, but it is not a definitional reduction: feasibility is not defined as low J; it is evaluated externally. The self-citations to GSC [43] and CompDiffuser [40] are baselines and prior compositional formulations, not load-bearing authorities that force the current result, and no uniqueness theorem is imported from the authors' prior work. The main legitimate concern is an implementation/evaluation mismatch: Appendix M (Algorithm 3) overwrites predicted next states with learned per-skill forward dynamics before applying the pruning metric, a component absent from Algorithm 1 and Section 3.1. This is a correctness/attribution risk for the TAMP results, but it is not a circular equivalence of a prediction to its inputs by construction. Accordingly, no circularity step meets the evidentiary bar, and the appropriate score is 0.

Axiom & Free-Parameter Ledger

3 free parameters · 6 axioms · 0 invented entities

All invented elements are algorithmic (elite search, curvature-based pruning), not physical entities; they are internal to the method. The main external grounding is task success in robotics, but the feasibility signal used for pruning is model-internal and not independently verified.

free parameters (3)
  • TAMP sampling hyperparameters (B, K, U_T, k_e, k_p, P) = B=50/100, K=0.2B, U_T=40/50, k_e=0.7, k_p=0.3, P=0.4T
    Per-task hand-tuned exploration/pruning schedule; performance improves monotonically with B and U (Fig. 14), so the reported success rates are conditional on these choices.
  • Image/video sampling hyperparameters (B, U_T, k_e, k_p, P, gamma) = B=10, U_T=10, k_e=0.2/0.3, k_p=0.5/0.6, P=0.5T, gamma=0.5
    Chosen per domain without a stated selection criterion; composition weights gamma_1:H are set to 0.5 for all segments.
  • lambda_t in guided sampling distribution = unspecified
    The modified transition p_J uses exp(-J/lambda_t), but lambda_t is never defined or used in Algorithm 1; the paper approximates the distribution by elite selection. This is an unspecified free schedule.
axioms (6)
  • domain assumption Bethe approximation (Eq. 1) represents p(tau) as a product of local factor distributions divided by marginals, with overlaps modeled as degree-2 variables.
    This is an approximation, not an exact factorization, and the paper does not quantify its error for multimodal local distributions.
  • ad hoc to paper Overlapping variable scores are approximated by the average of the two adjacent factor conditional scores (Sec. 2).
    The averaging is exactly what the paper says causes mode-averaging, so the method's own resampling is needed to counteract this approximation.
  • domain assumption A global plan is feasible iff all local transitions are feasible, and high likelihood under p(y) implies local feasibility (Sec. 3.1).
    The entire pruning criterion depends on the local diffusion model's likelihood being a faithful proxy for real-world feasibility.
  • ad hoc to paper DDIM-inversion curvature g(y) ranks samples by closeness to modes of p(y) (Eq. 5, App. D).
    Supported only by a 1D illustrative example; no theoretical or empirical analysis shows this holds for high-dimensional robot states or video latents.
  • ad hoc to paper For TAMP, per-skill learned forward dynamics models are available and overwrite predicted next states before pruning (App. M).
    This auxiliary correction is not part of the main algorithm and is disclosed only in the appendix; the reported TAMP results depend on it.
  • domain assumption Training data for each skill is diverse enough that precondition-effect overlaps between all skills needed for a plan exist (App. F.1).
    The authors state that if such overlap does not exist, CDGS cannot complete the plan; this is a data coverage assumption.

pith-pipeline@v1.3.0-alltime-deepseek · 29119 in / 14734 out tokens · 146394 ms · 2026-08-03T13:08:24.185770+00:00 · methodology

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read the original abstract

Generative models have emerged as powerful tools for planning, with compositional approaches offering particular promise for modeling long-horizon task distributions by composing together local, modular generative models. This compositional paradigm spans diverse domains, from multi-step manipulation planning to panoramic image synthesis to long video generation. However, compositional generative models face a critical challenge: when local distributions are multimodal, existing composition methods average incompatible modes, producing plans that are neither locally feasible nor globally coherent. We propose Compositional Diffusion with Guided Search (CDGS), which addresses this mode averaging problem by embedding search directly within the diffusion denoising process. Our method explores diverse combinations of local modes through population-based sampling, prunes infeasible candidates using likelihood-based filtering, and enforces global consistency through iterative resampling between overlapping segments. CDGS matches oracle performance on seven robot manipulation tasks, outperforming baselines that lack compositionality or require long-horizon training data. The approach generalizes across domains, enabling coherent text-guided panoramic images and long videos through effective local-to-global message passing. More details: https://cdgsearch.github.io/

Figures

Figures reproduced from arXiv: 2601.00126 by Danfei Xu, David He, Utkarsh A Mishra, Yongxin Chen.

Figure 1
Figure 1. Figure 1: Compositional Diffusion with Guided Search (CDGS) composes short-horizon plan dis￾tributions to sample long-horizon goal-directed plans directly at inference. Unlike na¨ıve composi￾tional sampling, it explores diverse plans and fil￾ters locally inconsistent paths to avoid “mode av￾eraging”, yielding globally coherent plans. Synthesizing coherent long sequences is a cru￾cial and challenging task, requiring … view at source ↗
Figure 2
Figure 2. Figure 2: Applications of CDGS. (Top) Long horizon motion planning: CDGS discovers a valid multi-step plan to move the blue cube to the green cube’s original position via : (1) using the hook to pull blue cube in workspace, (2) displace the green cube to make space and (3) moving the blue cube to the target position. (Mid) CDGS generates coherent panoramic images. (Bottom) CDGS can stitch short clips to generate con… view at source ↗
Figure 3
Figure 3. Figure 3: Running example. (a) Consider a 1D-domain of {x1:7} variable distributions and {y1:6} feasible directed transitions between the variables. There are two feasible long-horizon plans from start (x1) to goal (x7): one through the top and one through the bottom. (b) in naive-composition, sampled plans may choose to start in the top and end at the bottom, or vice versa. When this happens, the intermediate model… view at source ↗
Figure 4
Figure 4. Figure 4: Compositional diffusion with Guided Search. At each denoising timestep, CDGS it￾eratively denoises a batch of noisy candidate global plans by (i) iterative resampling to propagate information through averaged scores at overlaps (blue) and (ii) pruning candidates with local in￾consistencies based on the predicted clean samples (yellow). This process ensures all local plans align and belong to high-likelihoo… view at source ↗
Figure 5
Figure 5. Figure 5: Left: Visualizing plan pruning. When compositional sampling chooses an infeasi￾ble mode sequence, the resulting plan can hallucinate out-of-distribution transitions due to mode￾averaging as explained in Sec. 3. For instance, (a) Infeasible transitions: inhand(hook) precondition is never met for place(hook), and (b) State hallucination: cube moves under(rack) as a result of averaging toward the goal state, … view at source ↗
Figure 6
Figure 6. Figure 6: Panorama image generation. The above figure shows the qualitative comparison of CDGS with MD [4] and SD [33]. We show qualitative intuition behind global coherence and local feasibility: while SD generates smooth panoramas, they fail to satisfy the global context (mountain peak with skiers), on the other hand, MD follows the global context (beach in La La Land style) but fails to exhibit local consistency.… view at source ↗
Figure 7
Figure 7. Figure 7: Long video generation. CDGS w/ PR (below) maintains subject-consistency while CDGS w/o PR (top) exhibits mode-averaging, resulting in significant changes to the subjects’ appearances. sequences of frames are stitched to make a long video, a key challenge is maintaining subject con￾sistency and minimizing temporal artifacts. We use CogVideoX-2B [62] as the base model, capable of generating ∼ 50-frame videos… view at source ↗
Figure 8
Figure 8. Figure 8: This plot contrasts the DDIM Inversion (forward noising, blue lines) with DDIM Denois [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparing DDIM trajectories and associated OOD metrics. Left shows superimposed DDIM inversion (noising, blue) and denoising (reconstruction, red) paths. The blue lines show samples starting from both ID and OOD regions (e.g., the middle segment) being noised. The red lines show that all trajectories, when denoised, are guided back to the ID (green) regions. Bottom highlights the initial steps of the inver… view at source ↗
Figure 10
Figure 10. Figure 10: Hook Reach Task 2 3. Rearrangement Push (Task 1): • Scene: Table with a hook, cube, and rack • Start: Hook and cube are in workspace, rack is beyond workspace • Goal: Position the cube under the rack • Action Skeleton: pick(cube) → place(cube) → pick(hook) → push(cube, hook, rack) 4. Rearrangement Push (Task 2): • Scene: Table with a hook, cube, and rack • Start: Hook is in workspace, cube and rack are be… view at source ↗
Figure 11
Figure 11. Figure 11: Rearrangement Push Task 2 5. Rearrangement Memory (Task 1): 23 [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Rearrangement Memory Task 2 E.1 SKILL STRUCTURE We consider a finite set of parameterized skills in our skill library. The parameterization, data collection, and training method for each of the skills is described as follows: 1. Pick: Gripper picks up an object from the table and the parameters contain 4-DoF pose in the object’s frame of reference (x,y,z,θ). 2. Place: Gripper places an object at the targe… view at source ↗
Figure 13
Figure 13. Figure 13: Network architecture for the score function [PITH_FULL_IMAGE:figures/full_fig_p025_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: We show the effect of scaling B and U on the overall task planning and motion planning success of CDGS for shorter tasks (H = 4&5) in (a,b) and longer tasks (H = 7) in (c,d) and Task 2; Rearrangement Push Task 1; Rearrangement Memory Task 1) and longer H = 7 (Re￾28 [PITH_FULL_IMAGE:figures/full_fig_p028_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Hardware setup 29 [PITH_FULL_IMAGE:figures/full_fig_p029_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Left: runtime scales linearly with horizon length and resampling steps. Right: success [PITH_FULL_IMAGE:figures/full_fig_p036_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Comparison of time and success heatmaps for pruning [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: We show results for OGBench maze tasks. We observe that performance improves with [PITH_FULL_IMAGE:figures/full_fig_p037_18.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Energy-based Compositional Diffusion Planning

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    ECD reformulates compositional diffusion planning as energy minimization over local bridge potentials, adding a boundary reaction term and a Markov score approximation that runs in linear time.

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

    cs.RO 2026-05 unverdicted novelty 6.0

    XDiffuser combines extrinsic graph planning with diffusion models to guide denoising and improve performance on long-horizon robotic tasks including multi-agent coordination and TSP-style problems.

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