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CrossBFM: Distilling a Shared Latent Behavior Space Across Humanoid Embodiments

Tan-Dzung Do, Tuan Dat Phuong, Nico Bohlinger, Cuc T. Trinh, Siwei Ju, Vien Anh Ngo, Jan Peters, Xinchao Wang, An T. Le

arXiv:2609.38087v1cs.RO

TL;DR

BFMs provide a unified latent command for humanoid behaviors, but training is costly and independently trained robots have unrelated latent spaces. CrossBFM distills a frozen behavior space across embodiments using retargeted correspondences. Across three humanoids, the approach transfers the prompting modes, with latent-conditioned tracking within 0.025 rad of joint-conditioned tracking.

  • Problem

    BFMs require costly training, and independently trained robots receive unrelated latent spaces whose coordinates represent different behaviors.

    Source: §1 · p. 2

  • Method

    CrossBFM uses retargeted frame-level correspondences to distill a frozen source behavior space into a unified encoder without robot-specific parameters.

    Source: §1 · p. 2

  • Results

    Across three humanoids, distilled latents support tracking, smooth goal reaching, and reward prompting across 41 tasks, with tracking within 0.025 rad of joint-conditioned policies.

    Source: §5.1 · p. 7, §6 · p. 10

  • Takeaways & Limitations

    Training on a quarter of the motion corpus costs only 5% of tracking performance, while an encoder trained on other robots recovers up to 89.3% on an unseen, morphologically similar robot.

    Source: §5.3 · p. 8, §5.4 · p. 9

Abstract

from arXiv · show

Behavior Foundation Models (BFMs) give humanoids a promptable policy over a latent behavior space, enabling one single vector to represent a motion to imitate, a pose to reach, or a reward to maximize. Forward-Backward representations successfully produce such spaces, but at the cost of hundreds of GPU-hours for a single robot. Moreover, when the training process is repeated for a second robot, it produces a second space unrelated to the first, resulting in embodiment-specific latents that do not unify or transfer. We address these problems with CrossBFM, treating the latent space as the transferable asset for various embodiments. As retargeting provides frame-level cross-embodiment correspondence, we propose a unified encoder architecture with no robot-specific parameters for distilling the behavior space to address all training embodiments simultaneously in less than a GPU-hour. Following this encoder, latent-conditioned trackers turn the distilled latent into whole-body control in a conventional PPO training manner in just 10 more GPU-hours. On three distilled humanoids, all three prompting modes transfer: motion tracking with latent-conditioned policy losing only $0.025$ rad to its joint-conditioned counterpart, smooth goal reaching between poses with no falls, and reward optimization for all $41$ reward prompts. Our experiments further reveal that 1) regressing the encoder on a quarter of the motion corpus costs only $5\%$ of tracking performance and 2) training the encoder on a subset of robots and evaluating on an unseen one recovers up to $89\%$ of the tracking performance of seen robots, demonstrating cross-embodiment generalization to morphologically similar robots. We also verify the pipeline on real robots across all three prompting modes and with flow-based generated latents. Project website: https://dotandung.github.io/crossbfm/

1 INTRODUCTION

BFMs offer a single latent command for motion tracking, goal reaching, or reward optimization, but training is costly and separately trained robots receive unrelated latent spaces. CrossBFM distills a frozen behavior space across embodiments using retargeted correspondences, then trains latent-conditioned trackers.

1 INTRODUCTION

  • BFMs let one latent vector prompt motion tracking, goal reaching, or reward optimization without retraining, but a training run costs more than 100 GPU-hours.Separate robot-specific training produces latent spaces whose coordinates represent different behaviors, complicating cross-embodiment transfer.Source: §1 · p. 2
  • CrossBFM transfers a frozen source behavior space across robots by using retargeted motions as frame-level correspondences for supervised distillation.A unified encoder maps configurations from multiple robots into the shared space, replacing a separate training run for each embodiment.Source: §1 · p. 2
  • The unified encoder has no robot-specific parameters and distills across training embodiments in one run, while trackers use the resulting latents for whole-body control.The encoder uses a fixed-width proprioception view with masked indices for joints and key bodies absent from a robot.Source: §1 · p. 2
  • CrossBFM also reports real-robot transfer across the prompting modes and a flow-based latent generator for behavior modes.The authors describe the full pipeline as requiring around 10 hours on an RTX4090, compared with about 102 GPU-hours for source-model online unsupervised RL.Source: §1 · pp. 2–3

2 RELATED WORK

Prior work develops behavior spaces, cross-embodiment policies, state-space correspondences, and unified latent representations, but these approaches do not jointly retain a pretrained, value-functional behavior space across robots. CrossBFM instead transfers a frozen Forward–Backward space using retargeted data.

Behavior foundation models and unsupervised RL for humanoid control

  • Behavior foundation models build on Forward–Backward representations to map rewards, goals, or demonstrations to latent task descriptors, but existing spaces are robot-specific.Earlier systems include FB-CPR, BFM-Zero, and UFO; UFO cuts FB pre-training by five times to over 100 hours on a consumer GPU.Source: §2 · p. 3

Cross-embodiment learning

  • Cross-embodiment policies can generalize to unseen embodiments, but typically address a single task and share morphology representations rather than behavior spaces.Other methods align state spaces with optimal transport or graph matching, while CrossBFM leverages retargeted datasets as correspondences.Source: §2 · p. 3
  • Unified cross-embodiment latent-space methods learn descriptive latents from scratch, whereas CrossBFM inherits a frozen FB space with prompting semantics and closed-form reward-to-latent inference.Retargeted motions aligned on a shared timeline provide teacher–student correspondence for distilling that space.Source: §2 · p. 3

3 PRELIMINARIES

The preliminaries explain how successor measures represent policy dynamics and how Forward–Backward representations make that structure useful for reward-conditioned control. They then describe the three prompt types that CrossBFM seeks to preserve across embodiments.

3.1 UNSUPERVISED RL AND SUCCESSOR MEASURES

  • In reward-free unsupervised RL, a successor measure records where a policy goes over future steps, and the value function combines that measure with rewards at visited states.This separates policy dynamics from reward values and permits test-time evaluation of rewards without reward-driven fine-tuning.Source: §3.1 · p. 4

3.2 FORWARD–BACKWARD REPRESENTATIONS

  • Forward–Backward representations approximate the successor measure with forward and backward maps, and the backward map converts a reward function into its maximizing policy’s latent in closed form.The reward latent is obtained by averaging backward-map features weighted by reward over the state distribution.Source: §3.2 · p. 4

3.3 THE THREE PROMPTING MODES

  • The BFM supports motion tracking, goal reaching, and reward optimization prompts; transferring latents in the frozen source coordinate system preserves all three modes.The backward map’s closed-form mapping from desired behaviors to latents is why CrossBFM focuses on distilling that map.Source: §3.3 · p. 4

4 CROSSBFM

CrossBFM maps retargeted proprioception from multiple robots into the frozen source BFM’s latent space. It then trains latent-conditioned trackers and adapts prompting to support tracking, reaching, and reward optimization.

4.1 SETUP AND NOTATION

  • A frozen Unitree G1 BFM supplies source latents for frame-aligned retargeted motions, making target-side learning a regression into its latent coordinates.Retargeted clips preserve the same timeline and behavior across robots.Source: §4.1 · pp. 4–5

4.2 THE UNIFIED ENCODER ARCHITECTURE

  • The unified encoder maps a fixed-width, robot-independent representation of joints, key bodies, and pelvis proprioception across robot morphologies.Missing joint indices are zero-padded and flagged, distinguishing absent joints from joints at zero.Source: §4.2 · p. 5

4.3 STAGE 1: BACKWARD MAP REGRESSION

  • Just under an hour on one consumer GPU trains the encoder to map target proprioception into the frozen source latent space.The passage contrasts this with approximately 102 GPU-hours to train BS; causal attention restricts each frame to current and past frames for real-world control.Source: §4.3 · pp. 5–6

4.4 STAGE 2: LATENT-CONDITIONED POLICIES

  • Each robot’s PPO tracker conditions on the shared behavior latent and proprioception, without an explicit reference trajectory in the actor’s observation.A rectified-flow model trained on latent chunks supports prompts beyond robot-specific joint-space references.Source: §4.4 · p. 6

4.5 DEPLOYMENT: PROMPTING WITHOUT A TARGET-SIDE FB MODEL

  • Motion tracking and goal reaching obtain latents by encoding retargeted reference windows or windows ending at the goal pose.The deployment passage states these two prompting modes transfer immediately after encoder training.Source: §4.5 · p. 6
  • Reward optimization uses retargeted-dataset latents and key-body features, with percentile alignment adapting reward thresholds across robots.This alignment permits reward formulations to be computed for new robots without hand-crafting thresholds for each one.Source: §4.5 · pp. 6–7

5 EXPERIMENTS

The experiments test transfer across three target humanoids, unseen motions and robots, reduced distillation data, and real hardware. Across these settings, they evaluate whether a unified latent space supports the original prompting modes and generalizes beyond training examples.

5.1 TRANSFERRING THREE ORIGINAL PROMPTING MODES

  • Under the same training settings, latent-conditioned policies track reference motions across all three robots with a latent-minus-joint gap within 0.025 rad, despite receiving only one behavior latent.Computing zrew on the source robot with its true backward map BS is 3.5× and 3.0× worse than ours on M3 and N1, respectively; ours uses the cached retargeted dataset, percentile reward threshold, and feature transformation.Source: §5.1 · p. 7
  • Latent interpolation enables smooth goal reaching, with at most 0.032 rad cost relative to tracking performance; discontinuous joint-target jumps cause large torques and early termination.Source: §5.1 · p. 7

5.2 LATENT INFERENCE ON UNSEEN MOTIONS

  • On validation clips of represented behaviors, inferred latents incur 1.4–6.7 mm of key-body error while maintaining balance, and validation trajectories fall within their behavior clusters.The t-SNE visual compares source G1 and distilled M3 trajectories; dashed outlines mark unseen validation clips.Source: §5.2 · p. 8, Table 3 · p. 8, Figure 3 · p. 8

5.4 GENERALIZE TO UNSEEN ROBOTS

  • When trained without M3, the encoder recovers 89.3% of the all-robot tracking performance on M3, compared with 12.8% on unseen T1.The reported comparison trains on two robots and evaluates on the third using fixed pretrained trackers.Source: §5.4 · p. 9, Table 4 · p. 9

5.3 DATA SCALING: A QUARTER OF THE CORPUS SUFFICES

  • At 25% of the corpus, joint MAE rises from 0.2132 at 100% to 0.2241, a 5% degradation; performance begins breaking down at 10% (0.2706) versus 0.4411 for random latents.At one-quarter of the data, the distilled trajectories still preserve separated behavior classes, including validation clips.Source: §5.3 · p. 8, Figure 4 · p. 9

5.5 REAL-WORLD DEPLOYMENT

  • On real M3 and T1 robots, latent-conditioned tracking remains slightly behind joint-conditioned tracking, while goal reaching and reward optimization remain comparable to simulation with some degradation.Table 5 reports real-world tracking, goal-reaching, and reward-optimization results on M3.Source: §5.5 · pp. 9–10, Figure 5 · p. 9, Table 5 · p. 10

6 CONCLUSION

CrossBFM transfers a frozen source behavior space by using retargeted data as cross-embodiment correspondence and supervisedly distilling latents. Its conclusion reports a shared encoder, comparable latent-conditioned tracking, and successful prompting across robots, while the appendices describe robot configurations and a common encoder input.

6 CONCLUSION

  • CrossBFM distills a frozen source BFM’s latents through supervised learning on retargeted data, treating the shared dataset as cross-embodiment correspondence.The unified encoder has no per-robot parameters and trains in under a GPU-hour; latent-conditioned trackers support smooth goal reaching and zero-shot reward prompting across 41 tasks.Source: §6 · p. 10

A.1 ROBOT PLATFORMS

  • The experiment uses a frozen Unitree G1 source and three targets that differ from it and one another in DoF count, body count, joint names, and joint order.The targets are Inhouse M3, Booster T1, and Fourier N1.Source: §A.1 · p. 14, Table 6 · p. 14

A.2 THE ENCODER INPUT

  • The unified encoder receives the same 163 input dimensions for every robot, with presence masks marking entries as present or missing.Source: §A.2 · p. 14, Table 7 · p. 14

A.3 ENCODER ARCHITECTURE

The encoder is a shared sequence-to-sequence transformer designed to map canonical proprioception into source-space behavior latents across embodiments. Its architecture uses normalization and projection choices to prevent collapse and keep outputs on the source latent manifold.

A.3 ENCODER ARCHITECTURE

  • The sequence-to-sequence transformer maps a window of canonical proprioceptive frames to one latent per frame.Its configuration is summarized in Table 8.Source: §A.3 · p. 14, Table 8 · p. 15
  • Pre-LayerNorm prevents mode collapse, while projection onto the sphere keeps outputs on the frozen tracker’s latent manifold and allows gradients to flow through the projection.With post-LayerNorm, the model collapsed to a constant latent that the cosine objective could not recover.Source: §A.3 · p. 15
  • Fixed name maps, sign canonicalization, and robot-scale normalization provide universal input conventions without adding per-robot learned weights.Adding a robot then requires only a name map and scale constant, implemented as configuration rather than architecture changes.Source: §A.3 · p. 15

A.4 ENCODER TRAINING

  • For each optimizer step, the training sampler supplies the same motion window for every robot and supervises all robot views against a shared ground-truth latent.The protocol is described as encoder ablation training.Source: §A.4 · p. 15

A.5 TRACKER ARCHITECTURE AND TRAINING

Each embodiment has its own PPO tracking policy, with latent- and joint-conditioned variants trained under shared settings. The appendix also specifies domain randomization and the alignment, agreement, and closed-loop metrics used for evaluation.

A.5 TRACKER ARCHITECTURE AND TRAINING

  • The latent-conditioned tracker replaces reference-derived actor inputs with the frozen G1 latent, while the joint-conditioned variant uses the motion command’s joint targets.Rewards, terminations, randomization, PPO budget, and motion files are shared; the critic retains privileged future reference in simulation only.Source: §A.5 · pp. 15–16, Table 10 · p. 16, Table 11 · p. 17

A.6 DOMAIN RANDOMIZATION AND OBSERVATION NOISE

  • Both conditioning variants use identical training randomization, which is disabled during evaluation rollouts.The randomization settings are listed in Table 12.Source: §A.6 · p. 17, Table 12 · p. 17

B.1 METRICS

  • Alignment is validation cosine similarity to the frozen source latent, agreement is cosine similarity between two robots’ predictions on the same frame, and closed-loop metrics include joint MAE and root-frame key-body error.Joint MAE is measured in radians; key-body error is mean Euclidean distance in metres.Source: §B.1 · p. 17

B.2 REWARD OPTIMIZATION TASK SUITE

The appendix reports reward-suite evaluation setup and three encoder analyses: marginal transport for robot-specific reward thresholds, causal versus bidirectional encoding, and unified versus per-robot encoders. Causal encoding preserves tracking performance, while the unified encoder improves cross-robot latent agreement without sacrificing alignment.

B.2 REWARD OPTIMIZATION TASK SUITE

  • The reward suite comprises 41 G1 task rewards, evaluated using one inferred latent per task held constant for a 300-step episode.Scoring uses only the settled second half of each episode, after the robot reaches a stable pose.Source: §B.2 · pp. 17–18, Table 13 · p. 18

B.3 MARGINAL TRANSPORT

  • Marginal transport converts G1 reward thresholds to target-robot thresholds by matching their empirical quantiles, accommodating differences in reachable arm-tip heights.The G1 medium-band lower edge of 1.0 m is at quantile 0.938; that quantile sets the corresponding target threshold.Source: §B.3 · p. 18, Table 14 · p. 18

C.1 CAUSAL ENCODING FOR BEHAVIOR PREDICTION

  • 0.2043 vs 0.2068 rad joint MAE on the full corpus, and 0.2045 vs 0.2129 rad with 25% of the corpus: causal encoding matched or improved tracking over bidirectional encoding.On the full corpus, causal attention reduced validation cosine similarity by 0.0275; it also removes the need for future observations and enables real-time reference streaming.Source: §C.1 · pp. 18–19, Table 15 · p. 19

C.2 UNIFIED ENCODER VERSUS EMBODIMENT-SPECIFIC ENCODERS

  • The unified encoder produced greater agreement among three new robots than independently trained encoders, with similar alignment to the ground-truth latent.Reducing trunk width from H=512 to H=256 improved mean cosine by +0.010 (0.8548 → 0.8652), while H=128 degraded encoder performance.Source: §C.2 · p. 19, Table 16 · p. 19

C.3 SENSITIVITY TO RETARGETING ERROR

The sensitivity study tests whether errors in retargeted frame correspondence affect encoder training or inference. Timing offsets can be recovered by searching and shifting, while geometric corruption is tolerated only within limits.

C.3 SENSITIVITY TO RETARGETING ERROR

  • The study perturbed canonical proprioceptive inputs, testing geometry errors and timing offsets during both encoder training and inference while keeping trackers and reference motions unchanged.The tested errors included systematic joint bias, frame-wise Gaussian noise, constant timing offset, and per-clip timing offset.Source: §C.3 · pp. 19–20
  • A phase search recovered injected timing offsets exactly; after back-shifting, 8-, 16-, and 32-frame offsets yielded phase-aligned MAEs of 0.1646, 0.1641, and 0.1621 rad versus 0.1655 rad clean.With random per-clip timing offsets, performance remained poor even after back-shifting.Source: §C.3 · p. 20, Table 18 · p. 20
  • At σ=0.05, non-systematic geometric noise cost +0.002 rad at inference and +0.001 rad during training; systematic bias was harmless to roughly ×4 but degraded alignment and tracking by ×8.At ×8 bias, alignment fell from 0.8580 to 0.7647 and MAE rose from 0.1647 to 0.1913.Source: §C.3 · p. 20, Table 20 · p. 21

C.4 CROSS-EMBODIMENT GENERALIZABILITY EXPERIMENT PROTOCOL

The protocol compares nine encoders across three folds and three seeds, using the same validation clips for every robot.

C.4 CROSS-EMBODIMENT GENERALIZABILITY EXPERIMENT PROTOCOL

  • Nine encoders were evaluated across three folds and three seeds, with a shared validation split of 10 clips spanning all eight behaviors.The oracle, predicted, and random latent cells of Table 4 use the same harness and clip set; the random-latent floor was 0.3371 on M3 under this 10-clip rollout protocol.Source: §C.4 · p. 21

D FLOW-BASED MOTION GENERATOR

The flow-based generator samples latent trajectories in the shared behavior space, allowing its outputs to prompt all robots without reference motion or a robot-specific intermediate. The pipeline is evaluated in simulation and on real hardware across four prompt modes.

D FLOW-BASED MOTION GENERATOR

  • A conditional rectified-flow model generates chunks of 64 consecutive latents in the shared space, so one generator can prompt all embodiments.Its velocity model is a 6-layer, width-512 transformer with 8 heads and approximately 16M parameters.Source: D FLOW-BASED MOTION GENERATOR · p. 21
  • Mode prompts and 16 preceding latents form cross-attention memory, while frame-aligned retargeted features enter through a gated path.Each condition is independently dropped with probability 0.1 during training, allowing any subset of the three conditions at sampling time.Source: D FLOW-BASED MOTION GENERATOR · p. 21
  • The generator learns a flow-matching velocity from interpolated noise and latent chunks, then samples by integrating that velocity for 20 steps with classifier-free guidance.Radial projection is reapplied after each step, and long sequences are generated autoregressively using the last 16 generated frames as conditioning.Source: D FLOW-BASED MOTION GENERATOR · p. 21
  • Training uses latents already stored in the retargeted corpus, samples clips uniformly to equalize behavior exposure, and evaluates on held-out clips.Clips shorter than the 64-frame horizon are discarded; held-out clips test generalization to unseen motions rather than unseen windows from known motions.Source: D FLOW-BASED MOTION GENERATOR · pp. 21–22

E PIPELINE INFERENCE

  • The pipeline is evaluated in simulation and on real robots across all four prompt modes, including motion tracking, goal reaching, and reward optimization.Figures 7 and 8 show examples of motion tracking and goal reaching, and reward optimization tasks, respectively.Source: E PIPELINE INFERENCE · p. 22, Figure 7 · p. 22, Figure 8 · p. 23
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