Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models

1 Introduction

• Long-horizon manipulation requires reasoning about how action choices affect later actions and final goals, while the planning space can grow exponentially with task length.The motivating example requires choosing object placements and tool use that satisfy environmental constraints and the goal of placing an object under a rack.Source: §1 · p. 1
• Earlier learning approaches use task-specific meta-policies or discriminative skill-chaining functions that require exhaustive search, limiting generalization and scalability to longer skill sequences.The chaining functions evaluate whether a proposed skill can meet the next skill’s preconditions and ultimately achieve the task.Source: §1 · p. 1
• GSC learns skill-level probabilistic generative models and composes them to directly sample valid skill chains for a given plan skeleton.For each skill, it generates parameters and post-condition states that satisfy the next skill’s precondition, subject to the initial state, goal, and additional constraints.Source: §1 · p. 2
• GSC trains individual skill diffusion models, chains their distributions for unseen task skeletons, and uses classifier-based guidance for specified constraints at test time.The paper evaluates three challenging manipulation domains and reports closed-loop deployment on physical robot hardware.Source: §1 · p. 2

Task and Motion Planning

• Task-and-motion planning breaks problems into symbolically feasible subtask sequences and primitive skills, but relies on full observability and accurate dynamics, constraining practicality and scalability.Logic-geometric and hierarchical approaches address symbolic feasibility, while the paper opts for a learning-based framework.Source: §2 · p. 2

Learning to solve long-horizon tasks

• Skill-chaining methods model skill preconditions and effects, but many focus on single tasks; multi-task approaches remain discriminative, exhaustive, and vulnerable to cascading errors in long sequences.Agia et al. [11] use CEM with learned RL skill priors, but the passage notes deterministic priors, lack of multimodal solutions, and inability to account for additional planning constraints.Source: §2 · p. 3

Generative models for planning

• Existing diffusion planners synthesize state or action sequences but capture training-task solution distributions, whereas compositional generative planning combines skill models for unseen tasks and inference-time constraints.The paper situates its approach alongside Diffuser [39], Decision Diffuser [40], and Diffusion Policy [37].Source: §2 · p. 3

Problem formulation

• Given a symbolically feasible skeleton of skills and objects, the planning problem seeks continuous skill parameters that ensure geometric feasibility, successive preconditions, and the goal condition.Each skill parameter governs its desired motion from a state in the environment.Source: §3 · p. 3

Environment setup

• Expert policies provide state-action-next-state transitions for each skill, with the environment represented by fully observable object poses and sizes.The transitions follow each skill’s model Tπ from a current state and parameters to a next state.Source: §3 · p. 3

Diffusion models

• A diffusion model estimates an unknown data distribution by progressively adding Gaussian noise and then iteratively denoising samples to recover clean data.The noise levels increase monotonically during the forward process; the reverse process is represented by a stochastic differential equation.Source: §3 · p. 3
• The score function is the gradient of the log density of the noised distribution, and its estimate supports a denoised estimate of the original sample.Diffusion models can represent multimodal positive samples and support flexible sampling strategies with constraint handling.Source: §3 · pp. 3–4

• Given a symbolically feasible skill skeleton, GSC samples state transitions and skill parameters so the final state meets the goal; parallel sampling makes it skeleton-length agnostic.The framework samples all individual skill models in parallel during reverse denoising.Source: §4 · pp. 4, 6
• Each skill is represented by an unconditional diffusion model over state-action-state transitions, trained from per-skill demonstrations with a transformer and skill-relevant object ordering.The state-action-state distribution captures both the skill policy and transition dynamics.Source: §4 · p. 4
• To avoid myopic forward-only autoregressive chaining, GSC forms forward and backward conditional distributions whose shared state encodes skill affordability and transition feasibility.The resulting state of one skill must lie in the next skill's initial-state distribution, and vice versa.Source: §4 · pp. 4–5
• A dependency factor γ ∈ [0, 1] balances how much a skill transition's state is influenced by the subsequent skill versus the goal condition.The paper states that γ can be fixed at 0.5 or fine-tuned for each skill.Source: §4 · pp. 5–6
• Classifier-based guidance adds constraint likelihoods over selected state-action nodes, with gradients computed on noisy samples using denoised estimates.Constraints can depend on intermediate actions and states, and may be added as terms in the target sampling distribution.Source: §4 · pp. 5–6
• A success predictor Q(s, s′), trained using failure data, scores sampled candidate sequences to select the best parameter sequence.The predictor estimates a skill's execution success probability from the current and transitioned states.Source: §4 · p. 6

Toy domain

• Toy compositions use parallel skill-model sampling to select a compatible intermediate state, then test fixed-start, restricted-goal, and fixed-endpoint constraints.Fixing both initial and goal states yields a single solution in the toy domain.Source: §5 · p. 7, Figure 4 · p. 7

Long-horizon manipulation

• Across nine unseen TAMP tasks, GSC is better than or as good as search-based methods; Table 1 compares success rates over 100 trials per task.The evaluation uses success in 100 random environment executions as its comparison metric.Source: §5 · pp. 6–7, Table 1 · p. 7

Imposing additional constraints

• For constrained packing, task-agnostic placement objectives improve sequence accuracy and consistency, while GSC handles unseen test-time constraints.Table 2 compares GSC with and without task-agnostic constraint handling against relevant baselines.Source: §5 · p. 7, Figure 5 · p. 8, Table 2 · p. 8

Generalizing to unseen sequences

• GSC tests longer unseen dependencies by requiring both box and hook placement, and closed-loop Franka execution checks skill feasibility and resamples plans.Resampling occurs when the resulting state satisfies a future or previous skill's precondition.Source: §5 · p. 8

Importance of the forward and backward dependency

• γ=0 produces states inconsistent with the initial state, while γ=1 makes the model myopic; γ=0.5 achieves balanced performance.The figure illustrates these failure modes on a rearrangement-push rollout.Source: Figure 6 · p. 8, §5 · p. 8

Data collection

• About 5,000 successful transitions from a random agent train the diffusion models; the success-probability module also uses failure transitions.Data covers pick, place, push, and pull skills in scenes with varied object counts.Source: §6 · p. 9

Real-world setup

• The real-world setup uses a Franka Panda arm, overhead RealSense camera, and AprilTag-based object pose detection for scene reconstruction.The setup includes blocks, a rack, and a hook.Source: §6 · pp. 9–10, Figure 8 · p. 9

Real-world planning and execution

• Planning runs in the reconstructed simulator scene with pretrained simulation-trained models; planned parameters are executed on the robot, with scene updates before replanning.The Frankx controller generates smooth linear motion toward the desired gripper pose.Source: §6 · p. 10

7 Limitations

• GSC assumes a given skeleton and does not solve the complete TAMP problem, though it is compatible with any skeleton-planning method.The authors describe it as one segment of a unified TAMP framework.Source: §7 · p. 10
• Validation covers fully observable environments and low-dimensional system states represented by 6-DoF object poses.The framework has not been validated with partial observability in the stated evaluation scope.Source: §7 · p. 10
• The fixed primitive-skill set requires expert training data or pretrained models; incorporating skill-discovery frameworks is proposed as an extension.Source: §7 · p. 10

8 Conclusion

• GSC addresses TAMP tasks with given skeletons using skill-centric diffusion models.Source: §8 · p. 10
• It chains trained individual skill distributions into skeleton-specific distributions to generate long-horizon parameterized skill-plan sequences for unseen skeletons.Source: §8 · p. 10
• The authors report scalability, flexible planning, stronger constraint handling, and generalization to new scenarios, including perturbations and replanning.Source: §8 · p. 10

A Summary of the Algorithm

• The algorithm summary includes skeleton-sequence scoring, constraint handling, and denoising steps for noisy samples.The supplied algorithm fragments also identify a predefined skill library and individual skill diffusion score functions.Source: A Summary of the Algorithm · p. 15
• 128 reverse-diffusion steps are used for most tasks, balancing sampling time against the higher sample quality associated with more steps.The authors tested 256, 128, 64, and 50 steps; they set γ = 0.5 and α = 1 for tasks with planning constraints, while γ = 1 makes GSC equivalent to trivial policy rollout.Source: A Summary of the Algorithm · p. 15

B Additional Discussion

• Joint state-action-state transitions are described as less sensitive to state perturbations than state-only diffusion paired with inverse-dynamics actions.The latter approach can produce a distribution shift between sampled states and inferred actions, with cascading errors sensitive to sampled-state quality.Source: B Additional Discussion · p. 16

Hook Reach

• In the described tasks, the target box is out of workspace while the hook and rack are inside; each skeleton picks the hook, pulls the box, then picks and places it on the rack.Source: C Task Descriptions · p. 17

Constrained Packing

• In Constrained Packing Task 1, three workspace boxes are picked and placed on the rack in three repeated sequences; the goal is to place all boxes there without collision, with a blue block initially on the rack.Task 2’s scene has three boxes in the workspace and an empty rack.Source: C Task Descriptions · pp. 17–18
• The four-box constrained-packing variant extends the repeated pick-and-place skeleton to four boxes and targets all four on the rack without collision.Source: C Task Descriptions · p. 18, Figure 11 · p. 18

Rearrangement Push

• Rearrangement Push Task 1 has a box and hook in the workspace and rack outside; its goal is Box under Rack, with skeleton Pick Box, Place Box, Pick Hook, Push Box using Hook.Source: C Task Descriptions · p. 18
• Rearrangement Push Task 3 targets the blue box under a rack after red, yellow, and cyan boxes are picked and placed.The task has four boxes and the rack is outside the workspace.Source: C Task Descriptions · p. 19, Figure 14 · p. 19
• Task 4 chains pulling an out-of-workspace box into reach, picking and placing it, then pushing it under a rack.Its stated goal is both to pick the box and to get it under the rack; the task is described as having action dependency across two intervening skills.Source: C Task Descriptions · pp. 17, 19

D Additional Results

• The visualization shows convergence from Gaussian noise toward a valid solution.Source: D Additional Results · p. 20
• The authors present the visualization as an example of diffusion-model convergence.Source: D Additional Results · p. 20
• The figure traces reverse diffusion for Rearrangement Push Task 3 across 50 timesteps.Source: Figure 16 · p. 20