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arxiv: 2606.00837 · v1 · pith:OWTQAWITnew · submitted 2026-05-30 · 💻 cs.RO · cs.LG

Coarse-to-Fine Compositional Diffusion for Long-Horizon Planning

Byoungwoo Park , Utkarsh A. Mishra , Jaemoo Choi , Juho Lee , Yongxin Chen This is my paper

Pith reviewed 2026-06-28 18:22 UTC · model grok-4.3

classification 💻 cs.RO cs.LG
keywords diffusion modelscompositional generationlong-horizon planningrobotic planningvideo generationimage generationinference-time sampling
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The pith

CoFi produces globally coherent long-horizon outputs by first aligning local diffusion estimates into a shared coarse scaffold then restoring fine details at an intermediate noise level with the same pretrained prior.

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

The paper establishes that standard compositional diffusion enforces only local consistency between neighboring plans, which can still yield implausible global structures in long-horizon tasks. CoFi addresses this by separating the process into two stages: first aligning denoised local estimates around one shared coarse structure to form a global scaffold, then diffusing that scaffold to an intermediate noise level and denoising it again with the original short-horizon prior to recover local details. This approach is shown to improve both global coherence and local sample quality across robotic planning, panoramic image generation, and long video generation while using 2-8 times fewer denoiser calls than prior methods that rely on repeated propagation or inference-time optimization.

Core claim

CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence.

What carries the argument

Coarse-to-Fine Compositional Diffusion (CoFi) sampler, which separates global structure formation from local detail refinement at inference time.

If this is right

  • Locally compatible plans no longer form implausible global routes or task sequences.
  • Global coherence and local sample quality both improve over standard compositional baselines.
  • The method requires 2-8 times fewer denoiser evaluations than repeated propagation or optimization approaches.
  • The same procedure applies without modification to robotic planning, panoramic images, and long video generation.

Where Pith is reading between the lines

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

  • The two-stage separation could be applied to any pretrained diffusion prior whose training horizon is shorter than the target output length.
  • Choosing the intermediate noise level might be automated by monitoring when global scaffold statistics stabilize during the first stage.
  • The approach suggests that global structure can be imposed without retraining if the prior already encodes the right local statistics.

Load-bearing premise

Forcing alignment around a shared coarse structure will not destroy the local consistency properties of the pretrained short-horizon prior, and an intermediate noise level exists that lets the same prior restore fine details without erasing the imposed global scaffold.

What would settle it

Running the alignment stage on a short-horizon prior and measuring whether local consistency metrics drop sharply, or testing whether denoising the scaffold at the chosen intermediate noise level erases the global arrangement in held-out long-horizon examples.

Figures

Figures reproduced from arXiv: 2606.00837 by Byoungwoo Park, Jaemoo Choi, Juho Lee, Utkarsh A. Mishra, Yongxin Chen.

Figure 1
Figure 1. Figure 1: The global plan Y is obtained by composing over￾lapping local plans Xi . Diffusion models provide strong priors for generating structured data (Ho et al., 2020; Song et al., 2021), but many tasks require outputs beyond the scale on which these models are typically trained. For example, a robot may need to reach a distant goal by chaining short feasible motions into a long plan (Luo et al., 2026). Directly … view at source ↗
Figure 2
Figure 2. Figure 2: Scaling short-horizon priors by composition. A long structured global plan is built by composing overlapping local plans from a pretrained short-horizon prior. The goal is not only to enforce local consistency (e.g., smooth transitions between adjacent local plans), but also to preserve global coherence (e.g., a plausible route, task sequence, or subject identity over the full horizon). We aim for a simple… view at source ↗
Figure 3
Figure 3. Figure 3: Local guidance reduces boundary mismatch but leaving the global coherence under-specified. This makes the direct design of a tractable (and differentiable) compositional reward rt for both desired properties nontrivial, especially in high-dimensional plan spaces. For this reason, existing guided compositional samplers usually replace rt with local surrogates rt(Yt) := PN i=1 rˆt [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 5
Figure 5. Figure 5: Panoramic image generation. The coarse-to-fine procedure maintains a consistent global style across distant chunks. Baselines show abrupt changes or gradual style drift over the panorama. Compositional long-horizon robotic planning [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Robotic Planning. A coarse scaffold route is refined into a plausible task-level trajectory. Here, the strongest compositional baselines already find reasonable global routes, and the remaining failures likely come from inverse￾dynamics tracking (Luo et al., 2026). On Scene-Play, we improve over CDGS from 51% to 63%, where the gain suggests that the coarse scaf￾fold stage provides a more stable scaffold fo… view at source ↗
Figure 6
Figure 6. Figure 6: Long video generation. The coarse-to-fine procedure preserves subject appearance and scene structure over long temporal ranges. Baseline shows temporal drift along distant frames [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: NFE–performance Pareto comparison. We com￾pare performance against the NFE across the three domains. CoFi improves CDGS with 2–8× fewer NFE, substantially reducing computational overhead while improving global coherence and local sample quality. Inference cost [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: , and (right) no scaffold alignment with constant λt = 1. The top row shows the coarse scaffold Y c 0 , and the bottom row shows the refinement Y r 0 . Numbers below the images report the CLIP score. Diffusion step t 0.8 0.9 1.0 t t = 1 Linear decay Cosine decay [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Effect of refinement depth t ⋆ . We vary t ⋆ to measure the trade-off between global structure preservation and local detail recovery. Image metrics compare Intra-Style (global) with CLIP (local), while video metrics compare subject consistency (global) with frame-level aesthetic quality (local). The colored × denote generation from w/o scaffold alignment (i.e., Y r t ⋆=T ∼ N (0, Id) in (16)) and intermed… view at source ↗
Figure 11
Figure 11. Figure 11: PointMaze trajectory examples. Each row shows five evaluation tasks at increasing maze scale. Each color denotes a distinct local plan segment. • Scene (Play): A tabletop manipulation task with a robot gripper and multiple objects. The planning space is 14-dimensional, selected from the full 40-dimensional observation: gripper 3D position (indices 12–14), two object 3D positions (indices 19–21, 26–29), ob… view at source ↗
Figure 12
Figure 12. Figure 12: AntMaze trajectory examples. Each row shows five evaluation tasks at increasing maze scale. Each color denotes a distinct local plan segment. global plan factorizes over the factor graph as pt(Yt) ∝ Y N i=1 pt(Xi t ). (24) Since the local plans overlap, this product double-counts the shared boundary variables. The Bethe free energy (Yedidia et al., 2000, 2005) corrects for this overcounting by subtracting… view at source ↗
Figure 13
Figure 13. Figure 13: Scene-Play rollout examples. Each row shows keyframes from a successful rollout for one of the five predefined manipulation tasks. The robot gripper must reach, grasp, and reposition objects on the table according to the task-specific goal configuration. B.3 Panoramic Image Generation Task description. Given a text prompt, the task is to generate a wide panoramic image (512×4608) that maintains consistent… view at source ↗
Figure 14
Figure 14. Figure 14: Panoramic image results. Per-prompt coarse scaffold and refined output (full prompts in Appendix B.8). set t ⋆ = 0.7T (refinement begins from step 15) with stochasticity η = 1.0 and ramp blending. We generate 5 random seeds per prompt and report the mean and standard deviation across seeds. Metrics. Intra-LPIPS (Zhang et al., 2018) measures the mean pairwise LPIPS perceptual distance between all pairs of … view at source ↗
Figure 15
Figure 15. Figure 15: Long video results. Per-prompt coarse scaffold and refined output. Each strip shows frames 1, 69, 137, 205, 273 of the 273-frame composed video (full prompts in Appendix B.8). B.7 NFE Analysis We compare the number of function evaluations (NFE) across methods. Let T denote the total diffusion steps and N the number of local plans. • GSC : Each denoising step requires one forward pass per local plan. Total… view at source ↗
read the original abstract

Diffusion models provide strong priors for generating structured data, but many tasks require outputs beyond the scale on which these models are typically trained. Compositional generation addresses this by composing overlapping local plans from a pretrained short-horizon prior into a long-horizon output. However, standard composition primarily enforces agreement between neighboring local plans, yielding local consistency without directly specifying the global structure of the full composition. As a result, locally compatible plans may still form an implausible route, task sequence, or temporal evolution. Existing methods improve global coherence by repeatedly propagating local consistency signals or by adding inference-time optimization, but these procedures become expensive as the number or dimensionality of local plans increases. We propose Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that separates global structure formation from local detail refinement. CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence. Across long-horizon robotic planning, panoramic image generation, and long video generation, CoFi not only improves both global coherence and local sample quality over prior compositional baselines, but also requires 2-8x fewer denoiser evaluations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that first aligns local denoised estimates from a pretrained short-horizon diffusion prior around a shared coarse structure to form a global scaffold, then diffuses this scaffold to an intermediate noise level and reapplies the same prior to restore fine details while preserving global coherence. It claims this yields better global coherence and local sample quality than prior compositional baselines across long-horizon robotic planning, panoramic image generation, and long video generation, while requiring 2-8x fewer denoiser evaluations.

Significance. If the intermediate noise level can be shown to reliably exist and generalize, the approach would provide an efficient way to extend short-horizon diffusion priors to long-horizon tasks without retraining or expensive inference-time optimization, addressing a practical bottleneck in compositional generation for robotics and sequential data.

major comments (1)
  1. [Abstract] Abstract (method description): The second stage relies on the existence of an intermediate noise level at which the pretrained local prior can add fine structure without erasing the imposed global scaffold; no equation, noise schedule, selection procedure, or ablation is supplied to characterize this level, demonstrate its stability under perturbation, or show that a single choice works across tasks without retuning.
minor comments (1)
  1. [Abstract] The abstract states performance and efficiency gains but supplies no quantitative tables, error analysis, or baseline comparisons that would allow verification of the 2-8x claim or assessment of variance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive comment. We address the concern about the intermediate noise level below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (method description): The second stage relies on the existence of an intermediate noise level at which the pretrained local prior can add fine structure without erasing the imposed global scaffold; no equation, noise schedule, selection procedure, or ablation is supplied to characterize this level, demonstrate its stability under perturbation, or show that a single choice works across tasks without retuning.

    Authors: We agree that the manuscript does not supply an explicit equation, noise schedule, selection procedure, or ablation study characterizing the intermediate noise level used in the second stage. In the revised version we will add these elements to the method section and abstract: an equation defining the target noise level, the fixed schedule employed, the selection procedure (based on matching scaffold scale to the prior's effective receptive field on a small validation set), and an ablation demonstrating stability under small perturbations as well as consistency of the same level across the three evaluated tasks. revision: yes

Circularity Check

0 steps flagged

No circularity; CoFi is a novel inference-time procedure

full rationale

The paper presents CoFi as a new two-stage sampling algorithm that first aligns local denoised estimates to form a global scaffold and then diffuses to an intermediate noise level for refinement with the pretrained prior. No equations, fitted parameters, or self-citations are shown that reduce the claimed global coherence or efficiency gains to a self-referential definition or input by construction. The intermediate noise level is an explicit design choice whose existence is assumed rather than derived from prior results in the paper itself. This is a standard non-circular presentation of a sampling method.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that a single pretrained short-horizon prior remains effective when applied at both coarse alignment and intermediate-noise refinement stages; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption A pretrained short-horizon diffusion prior can be reused effectively at an intermediate noise level to restore local structure after global alignment.
    The method description relies on this reuse without additional training or adaptation.

pith-pipeline@v0.9.1-grok · 5783 in / 1299 out tokens · 21003 ms · 2026-06-28T18:22:44.800799+00:00 · methodology

discussion (0)

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Reference graph

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12 extracted references · 3 canonical work pages · 1 internal anchor

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    and the refinement stage (Algorithm 2). After each denoising step, the composed global trajectory is obtained by exponentially blending adjacent segments in their overlap regions (Luo et al., 2026). Concretely, 13 Table 4: Environment specifications for robotic planning. Environment obs dim goal dim horizon overlapNreplan thres max steps PointMaze-Medium2...

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    Each color denotes a distinct local plan segment

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