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arxiv: 2605.04525 · v2 · pith:PBNCXZFNnew · submitted 2026-05-06 · 💻 cs.RO

HDFlow: Hierarchical Diffusion-Flow Planning for Long-horizon Tasks

Nandiraju Gireesh , Yuanliang Ju , Chaoyi Xu , Weiheng Liu , Yuxuan Wan , He Wang This is my paper

Pith reviewed 2026-05-20 23:33 UTC · model grok-4.3

classification 💻 cs.RO
keywords hierarchical planningdiffusion modelsrectified flowlong-horizon tasksrobot manipulationfurniture assemblygenerative planning
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The pith

HDFlow uses high-level diffusion for subgoals and low-level rectified flow for trajectories to plan long-horizon robot tasks more effectively.

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

The paper presents HDFlow as a hierarchical planning framework that pairs a diffusion model to generate sequences of strategic subgoals in latent space with a rectified flow model to produce smooth dense trajectories from those subgoals. This split exploits diffusion's strength in exploration while using the speed of ODE-based generation to meet real-time demands that single-paradigm planners often miss. The approach is tested on four furniture assembly tasks in both simulation and real robots, where it outperforms prior methods, and is shown to generalize across two additional long-horizon benchmarks mixing locomotion and manipulation.

Core claim

HDFlow is a novel hierarchical planning framework that employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's exploratory capabilities, and these subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories by exploiting the efficiency of ordinary differential equation-based trajectory generation.

What carries the argument

The two-level hierarchy in which high-level diffusion produces subgoal sequences in latent space to steer low-level rectified flow for dense trajectory generation.

If this is right

  • The method achieves significant outperformance over state-of-the-art planners on four challenging furniture assembly tasks in both simulation and real-world settings.
  • HDFlow generalizes to two long-horizon benchmarks that include diverse locomotion and manipulation tasks.
  • Using ODE-based generation at the low level reduces the computational cost of iterative denoising and supports more real-time execution.
  • The hierarchical decomposition supplies a principled way to handle sparse-reward long-horizon tasks that single-level generative planners struggle with.

Where Pith is reading between the lines

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

  • Adding intermediate levels between the current high- and low-level planners could further extend the approach to tasks with even longer horizons.
  • The learned latent space for subgoals may support transfer of plans across different robot embodiments or task distributions.
  • Explicit mechanisms for detecting when a subgoal cannot be reached and replanning at the high level would strengthen robustness in noisy real-world settings.

Load-bearing premise

Subgoals generated by the high-level diffusion planner will reliably guide the low-level rectified flow planner to produce successful trajectories without any explicit translation mechanism or failure recovery.

What would settle it

If the low-level rectified flow planner routinely produces invalid or unsuccessful trajectories when conditioned on the high-level subgoals, or if HDFlow fails to outperform state-of-the-art methods on the furniture assembly tasks, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.04525 by Chaoyi Xu, He Wang, Nandiraju Gireesh, Weiheng Liu, Yuanliang Ju, Yuxuan Wan.

Figure 1
Figure 1. Figure 1: HDFlow pipeline. The framework consists of two main stages: World Model Learning (left), where observations are encoded into a structured latent space, and Hierarchical Planner Training (right). The latter involves a High-Level diffusion planner generating sparse strategic subgoals (z1, . . . , zK) with Manifold-aware EBM guidance, and a Low-Level rectified flow planner synthesizing dense trajectories τ = … view at source ↗
Figure 2
Figure 2. Figure 2: Manifold-Aware EBM-Guided Diffusion step: Start￾ing from a noisy latent sample (zℓ), the standard reverse diffusion predicts a mean. EBM guidance (red arrow) then shifts this mean, leading to a guided sample (z temp ℓ−1 ). To prevent manifold devia￾tion, z temp ℓ−1 is subsequently projected onto the local latent mani￾fold Mℓ−1 (using local manifold approximation and projection, indicated by purple and gree… view at source ↗
Figure 3
Figure 3. Figure 3: (left) Real-world FurnitureBench setup. (right) A successful rollout of HDFlow planner on the one_leg assembly task initialized with Med randomness in both simulation (top) and real-world (bottom). Contribution of Core Components. We investigate the im￾pact of the contrastive world model, EBM guidance, and manifold projection by progressively removing them from HDFlow view at source ↗
Figure 4
Figure 4. Figure 4: Overview of tasks from FurnitureBench in simulation. FurnitureBench (Heo et al., 2025) is a novel furniture assembly benchmark for testing complex, long-horizon manipulation tasks. We choose a subset of 4 tasks from the available 9 tasks in the benchmark. The tasks involve assembling various pieces of furniture from individual parts using a simulated Franka Emika Panda robot in a IsaacGym environment. The … view at source ↗
Figure 4
Figure 4. Figure 4: Overview of tasks from FurnitureBench in simulation. FurnitureBench (Heo et al., 2025) is a novel furniture assembly benchmark for testing complex, long-horizon manipulation tasks. We choose a subset of 4 tasks from the available 9 tasks in the benchmark. The tasks involve assembling various pieces of furniture from individual parts using a simulated Franka Emika Panda robot in a IsaacGym environment. The … view at source ↗
Figure 5
Figure 5. Figure 5: RLBench Manipulation Tasks. We evaluate HDFlow on 18 simulated RLBench tasks, covering 249 variations of object poses, goal configurations, and scene appearances. During evaluation, the robot must complete each task under randomized colors, shapes, sizes, and semantic arrangements. Data Generation. Following the methodology of PerAct (Shridhar et al., 2023) and the capabilities of RLBench (James et al., 20… view at source ↗
Figure 5
Figure 5. Figure 5: RLBench Manipulation Tasks. We evaluate HDFlow on 18 simulated RLBench tasks, covering 249 variations of object poses, goal configurations, and scene appearances. During evaluation, the robot must complete each task under randomized colors, shapes, sizes, and semantic arrangements. sweep to dustpan, and turn tap. These tasks often involve variations in object colors, sizes, shapes, counts, and placements, … view at source ↗
Figure 6
Figure 6. Figure 6: OGBench Tasks. We evaluate HDFlow on 14 simulated OGBench tasks. • Maze Tasks: – navigate datasets: These datasets are considered successful and are collected by a noisy expert policy that navigates the maze by repeatedly reaching randomly sampled goals. – stitch datasets: These datasets are considered failure episodes and consist of short goal-reaching trajectories (at most 4 cell units long), designed to… view at source ↗
Figure 6
Figure 6. Figure 6: OGBench Tasks. We evaluate HDFlow on 14 simulated OGBench tasks. Data Generation. For each task, we generate both successful and failure episode data using different dataset types provided by the original benchmark: • Maze Tasks: – navigate datasets: These datasets are considered successful and are collected by a noisy expert policy that navigates the maze by repeatedly reaching randomly sampled goals. – s… view at source ↗
Figure 7
Figure 7. Figure 7: A successful rollout of HDFlow planner on the one_leg assembly task initialized with Low randomness. 25 view at source ↗
Figure 8
Figure 8. Figure 8: A successful rollout of HDFlow planner on the one_leg assembly task initialized with Med randomness. Initial state Grasp tabletop Place it to corner Pick up leg Insert leg Screw leg One Leg High view at source ↗
Figure 9
Figure 9. Figure 9: A successful rollout of HDFlow planner on the one_leg assembly task initialized with High randomness. 26 view at source ↗
Figure 10
Figure 10. Figure 10: A successful rollout of HDFlow planner on the round_table assembly task initialized with Low randomness. Initial state Grasp base Place it to corner Pick up bulb Insert bulb Screw bulb Pick up hood Place on the top of base Lamp Low view at source ↗
Figure 11
Figure 11. Figure 11: A successful rollout of HDFlow planner on the lamp assembly task initialized with Low randomness. 27 view at source ↗
Figure 12
Figure 12. Figure 12: A successful rollout of HDFlow planner on the lamp assembly task initialized with Med randomness. Initial state Grasp cabinet box Place it to corner Pick up and insert door Repeat with another door Make box stand up Pick up cabinet top Insert and Screw top Cabinet Low view at source ↗
Figure 13
Figure 13. Figure 13: A successful rollout of HDFlow planner on the cabinet assembly task initialized with Low randomness. 28 view at source ↗
Figure 14
Figure 14. Figure 14: A successful rollout of HDFlow planner on the one_leg assembly task initialized with Low randomness in the real-world. Initial state Grasp base Place it to corner Pick up bulb Insert bulb Screw bulb Pick up hood Place on the top of base Lamp Low view at source ↗
Figure 15
Figure 15. Figure 15: A successful rollout of HDFlow planner on the lamp assembly task initialized with Low randomness in the real-world. Initial state Grasp tabletop Place it to corner Pick up leg Insert leg Screw leg Pick up base Insert and Screw base Round Table Low view at source ↗
Figure 16
Figure 16. Figure 16: A successful rollout of HDFlow planner on the round_table assembly task initialized with Low randomness in the real-world. 29 view at source ↗
read the original abstract

Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce Hierarchical Diffusion-Flow (HDFlow), a novel hierarchical planning framework that optimally leverages the strengths of diffusion and rectified flow models to overcome the limitations of single-paradigm generative planners. HDFlow employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate HDFlow on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/

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

2 major / 1 minor

Summary. The paper introduces Hierarchical Diffusion-Flow (HDFlow), a hierarchical planning framework for long-horizon robotic tasks. A high-level diffusion model generates sequences of subgoals in a learned latent space to leverage exploratory capabilities, while a low-level rectified flow model uses ODE-based generation to produce smooth dense trajectories. The authors claim significant outperformance over state-of-the-art methods on four furniture assembly tasks in both simulation and real-world settings, plus generalizability on two long-horizon benchmarks involving locomotion and manipulation.

Significance. If the empirical results and hierarchical interface hold under scrutiny, HDFlow would demonstrate a practical way to combine diffusion's strength in subgoal exploration with rectified flow's efficiency for trajectory generation, addressing computational bottlenecks in real-time long-horizon planning. This could advance hierarchical generative planning in robotics by providing a principled decomposition rather than monolithic models.

major comments (2)
  1. [Abstract] Abstract: the central claim that HDFlow 'significantly outperforms state-of-the-art methods' on four furniture assembly tasks supplies no quantitative metrics, success rates, baseline comparisons, or statistical details. This absence directly undermines evaluation of the data-to-claim link for the primary empirical contribution.
  2. [Method section] Method section (hierarchical planner description): the mechanism by which latent-space subgoals from the high-level diffusion planner condition or are translated into inputs for the low-level rectified flow planner's ODE solver is not specified. No decoding step, conditioning variable, projection, or recovery policy is described, which is load-bearing for whether the hierarchical decomposition itself drives the reported successes rather than task-specific tuning.
minor comments (1)
  1. [Abstract] The abstract and introduction could more explicitly reference the project website for supplementary videos or code to aid reproducibility assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating the revisions we plan to make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that HDFlow 'significantly outperforms state-of-the-art methods' on four furniture assembly tasks supplies no quantitative metrics, success rates, baseline comparisons, or statistical details. This absence directly undermines evaluation of the data-to-claim link for the primary empirical contribution.

    Authors: We agree that the abstract would be strengthened by including specific quantitative metrics to support the performance claims. In the revised version, we will update the abstract to report key success rates (e.g., average success rate across the four tasks) along with direct comparisons to the strongest baselines and note the statistical significance of the improvements, while preserving the abstract's brevity. revision: yes

  2. Referee: [Method section] Method section (hierarchical planner description): the mechanism by which latent-space subgoals from the high-level diffusion planner condition or are translated into inputs for the low-level rectified flow planner's ODE solver is not specified. No decoding step, conditioning variable, projection, or recovery policy is described, which is load-bearing for whether the hierarchical decomposition itself drives the reported successes rather than task-specific tuning.

    Authors: We acknowledge that the interface between the high-level diffusion planner and the low-level rectified flow planner requires a more explicit and self-contained description. We will add a dedicated paragraph and accompanying equations in the Method section that detail the decoding of latent subgoals into state-space targets, the exact conditioning variables passed to the ODE solver, and the projection step used to initialize the trajectory generation. This revision will make clear how the hierarchical structure contributes to the overall performance. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical claims rest on external task evaluations

full rationale

The paper presents HDFlow as a hierarchical planner that uses a high-level diffusion model to produce latent subgoals which then condition a low-level rectified-flow ODE solver. All performance claims are grounded in reported results on four furniture-assembly tasks (sim and real) plus two long-horizon locomotion/manipulation benchmarks. No equations, fitted parameters, or first-principles derivations appear in the supplied text; the central argument is therefore an empirical comparison rather than a self-referential reduction of outputs to inputs. The subgoal-to-trajectory interface is described at a high level but is not asserted as a mathematical identity or prediction derived from the same data used to train the models. Consequently the derivation chain does not collapse by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the method implicitly assumes a learnable latent space and effective subgoal guidance but provides no details.

pith-pipeline@v0.9.0 · 5744 in / 1083 out tokens · 45395 ms · 2026-05-20T23:33:55.352110+00:00 · methodology

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discussion (0)

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Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages · 3 internal anchors

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    Forward Process and Conditional Score.The forward diffusion process defines how a clean latent state z0 is noised toz ℓ at timestepℓ: zℓ = √¯αℓz0 + √ 1−¯αℓϵ, ϵ∼ N(0,I) From this, the conditional distribution q(z0|zℓ) can be expressed as a Gaussian with mean µ(zℓ, ℓ) = 1√¯αℓ (zℓ −√1−¯αℓϵ) and variance Σ(ℓ) = (1−¯αℓ)I. The gradient of the log-probability of...

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    True Optimal Energy Guidance.The true optimal energy guidance, ∇zℓ Etrue(zℓ|c), aims to steer the diffusion process towards regions of low energy (high success probability) in the z0 space. This gradient is given by the expectation of the score of q(z0|zℓ) weighted by the exponential of the negative energy function, effectively performing importance sampl...

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    Learned EBM Guidance.Our learned EBM guidance, ∇zℓ Eϕ(zℓ|c), typically approximates the gradient of the energy function at zℓ. In many practical implementations, this effectively corresponds to a linear weighting of the score of q(z0|zℓ)by the energy function itself, rather than its exponential: ∇zℓ Eϕ(zℓ|c)≈E q(z0|zℓ)[E(z0|c)∇zℓ logq(z 0|zℓ)] =− 1√1−¯αℓ ...

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    Analysis of the Guidance Gap.The EBM guidance gap is defined as ∆EBM(zℓ) =∥∇ zℓ Etrue(zℓ|c)− ∇ zℓ Eϕ(zℓ|c)∥2. Substituting the expressions, we get: ∆EBM(zℓ) = − 1√1−¯αℓ Eq(z0|zℓ)[ϵ|e−E(z0|c)]−E q(z0|zℓ)[E(z0|c)ϵ] 2 14 HDFlow: Hierarchical Diffusion-Flow Planning for Long-horizon Tasks Let δ(z0) = e−E(z0 |c) Eq(z0 |zℓ )[e−E(z0 |c)] −E(z 0|c) represent the ...

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    This is achieved by combining classifier-free guidance for the conditional termp(z|c) and EBM guidance for the success termp(y= 1|z, c), as detailed in Proof A.3

    The guided sampling step samples from p(y= 1|z, c)p(z|c) , implementing the unconstrained Bayesian posterior. This is achieved by combining classifier-free guidance for the conditional termp(z|c) and EBM guidance for the success termp(y= 1|z, c), as detailed in Proof A.3

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    The projection step enforces the manifold constraint z∈ M by mapping to the closest point on the approximated manifold. By the principle of alternating projections and the contraction property of projection operators, this two-step process converges to a point that balances optimality (high success probability) with feasibility (remaining on the manifold)...

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    The RSSM is crucial for learning a recurrent state that summarizes the history of observations and predicts future states, which is vital for long-horizon planning

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    The RSSM, especially with the contrastive and IDM objectives, is specifically designed to create a latent space that is optimized for downstream planning

    Unstructured Latent Space:While DINOv2 provides semantically rich visual features, its latent space is not explicitly structured for planning in terms of task progress or action relevance. The RSSM, especially with the contrastive and IDM objectives, is specifically designed to create a latent space that is optimized for downstream planning

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    The RSSM acts as a bottleneck and a learning mechanism to extract the most pertinent information for control

    Dimensionality and Noise:Raw DINOv2 features might be higher dimensional or contain more irrelevant noise for planning compared to the compressed and refined latent states learned by the RSSM. The RSSM acts as a bottleneck and a learning mechanism to extract the most pertinent information for control. In conclusion, while DINOv2 serves as an excellent vis...

    work page