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arxiv: 2605.04525 · v1 · submitted 2026-05-06 · 💻 cs.RO

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

Nandiraju Gireesh , Yuanliang Ju , Chaoyi Xu , Weiheng Liu , Yuxuan Wan , He Wang
Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:22 UTC · model grok-4.3

classification 💻 cs.RO
keywords hierarchical planningdiffusion modelsrectified flowlong-horizon tasksrobotic planninggenerative modelstrajectory generationfurniture assembly
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The pith

HDFlow uses a high-level diffusion planner to generate subgoals in latent space and a low-level rectified flow planner to produce trajectories for long-horizon robotic tasks.

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 framework that pairs diffusion models for generating sequences of strategic subgoals with rectified flow models for creating smooth trajectories from those subgoals. This setup exploits diffusion's ability to explore in a learned latent space at the high level while using the efficiency of ODE-based generation at the low level to address the computational cost and lack of structure in earlier single-model generative planners. A sympathetic reader would care because long-horizon tasks with sparse rewards remain difficult for robots to plan and execute reliably in both simulation and the real world. The authors demonstrate that this combination yields better results than prior methods on specific assembly problems and extends to broader locomotion and manipulation benchmarks.

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 speed and efficiency of ordinary differential equation-based trajectory generation.

What carries the argument

The Hierarchical Diffusion-Flow planner, which decomposes planning into a diffusion-based high-level subgoal generator operating in latent space and a conditioned rectified flow-based low-level trajectory generator.

If this is right

  • HDFlow significantly outperforms state-of-the-art methods on four challenging furniture assembly tasks in both simulation and real-world settings.
  • The approach generalizes to two long-horizon benchmarks that include diverse locomotion and manipulation tasks.
  • High-level diffusion enables better exploration of subgoal sequences while low-level rectified flows deliver faster, smoother trajectory execution.
  • Real-time execution becomes more practical because the low-level planner avoids iterative denoising.

Where Pith is reading between the lines

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

  • If the separation of exploration at high level and efficiency at low level proves reliable, similar pairings of generative models could be tested on other robot control problems that mix discrete decisions with continuous motion.
  • Adding explicit feasibility verification between levels might be needed for tasks where unreachable subgoals occur more often than in the evaluated benchmarks.
  • The framework could connect to existing hierarchical reinforcement learning approaches that also separate abstract planning from low-level control.
  • Testing the method on tasks with even longer horizons or higher uncertainty would clarify how far the current latent-space conditioning scales.

Load-bearing premise

The learned latent space and subgoal conditioning allow the low-level rectified flow planner to generate feasible trajectories without additional feasibility checks or recovery mechanisms when high-level subgoals are unreachable.

What would settle it

Frequent generation of unsafe or incomplete trajectories on real-world furniture assembly trials when the high-level planner outputs subgoals that the low-level planner cannot reach directly from the current state.

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 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 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 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 HDFlow, a hierarchical planning framework for long-horizon robotic tasks that uses a high-level diffusion model to generate sequences of subgoals in a learned latent space and a low-level rectified flow model to produce smooth trajectories via ODE integration. It claims to significantly outperform state-of-the-art methods on four furniture assembly tasks in both simulation and real-world settings while also generalizing to two long-horizon benchmarks involving diverse locomotion and manipulation tasks.

Significance. If the empirical claims hold with robust quantitative support, the work could meaningfully advance hierarchical generative planning by combining diffusion's exploratory strengths with the computational efficiency of rectified flows, addressing real-time execution challenges in sparse-reward settings. The approach offers a potential template for decomposing long-horizon problems without relying on a single generative paradigm.

major comments (2)
  1. Abstract: the central claim of significant outperformance on four furniture assembly tasks (and generalization to benchmarks) is presented without any quantitative results, error bars, ablation studies, training details, or failure mode analysis, rendering the empirical contribution unverifiable from the manuscript text.
  2. Method (high-level to low-level interface): the framework relies on the assumption that subgoals generated by the diffusion planner in latent space are always reachable by the low-level rectified flow planner through ODE integration, yet no feasibility checks, replanning triggers, or recovery mechanisms are described; this is load-bearing for the long-horizon claims, as unreachable subgoals would cause low-level failures.
minor comments (1)
  1. Abstract: the wording 'optimally leverages the strengths' is imprecise and should be replaced by a concrete description of the division of labor between diffusion and flow components.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our submission. We address each major comment below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: Abstract: the central claim of significant outperformance on four furniture assembly tasks (and generalization to benchmarks) is presented without any quantitative results, error bars, ablation studies, training details, or failure mode analysis, rendering the empirical contribution unverifiable from the manuscript text.

    Authors: We acknowledge that the abstract, by design as a concise overview, omits specific quantitative details. The full manuscript contains these elements (error bars, ablations, training hyperparameters, and failure cases) in Sections 4–6. To address the concern directly, we will revise the abstract to include key quantitative results, such as average success rates and relative improvements over baselines on the furniture assembly tasks. revision: yes

  2. Referee: Method (high-level to low-level interface): the framework relies on the assumption that subgoals generated by the diffusion planner in latent space are always reachable by the low-level rectified flow planner through ODE integration, yet no feasibility checks, replanning triggers, or recovery mechanisms are described; this is load-bearing for the long-horizon claims, as unreachable subgoals would cause low-level failures.

    Authors: This is a fair observation. The latent space is jointly trained so that high-level subgoals lie within the distribution of states reachable by the low-level flow model, providing implicit alignment. However, the original manuscript does not explicitly describe feasibility verification or recovery procedures. We will add a dedicated paragraph in the Method section clarifying the high-to-low interface and introduce a lightweight recovery mechanism (high-level replanning triggered if the low-level ODE solver fails to reach the subgoal within a distance threshold after a fixed number of integration steps). revision: yes

Circularity Check

0 steps flagged

No circularity: framework combines existing models without self-referential derivations or fitted predictions

full rationale

The paper introduces HDFlow as a hierarchical architecture using a high-level diffusion planner for subgoals in latent space and a low-level rectified flow planner for trajectories via ODE integration. No equations, derivations, or first-principles results are presented that reduce to inputs by construction. Claims rest on empirical evaluation of the combined framework on furniture assembly and locomotion tasks, leveraging known properties of diffusion and flow models without renaming known results, smuggling ansatzes via self-citation, or treating fitted parameters as predictions. The central premise is a design choice, not a derived equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the hierarchical split and latent-space subgoal generation are presented as design choices whose justification is not detailed.

pith-pipeline@v0.9.0 · 5513 in / 1097 out tokens · 20947 ms · 2026-05-08T16:22:31.381940+00:00 · methodology

discussion (0)

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Reference graph

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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 13 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

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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

    Lack of Temporal Dynamics: DINOv2, while excellent for static visual representation, does not inherently capture temporal dynamics. 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...