Motion Diffusion Models (MDMs) can generate diverse and visually appealing human motion; yet, the resulting trajectories frequently violate physical constraints, limiting their downstream use in simulation and control. We present PhysibleMDM, a framework that promotes physical feasibility of MDM output by optimizing at inference time the diffusion noise without retraining the generative model. We introduce a set of surrogate feasibility constraints that can be evaluated without full trajectory simulation. These constraints combine kinematic checks (e.g., ground penetration, slip, and self-collision) with dynamic feasibility tests computed via an inverse-dynamics inner loop formulated as a cone program. We solve the resulting black-box noise optimization problem using the Separable Covariance Matrix Adaptation Evolution Strategy (Sep-CMA-ES), thereby avoiding reliance on computationally expensive and discontinuous gradients. An autoregressive scheme then chains optimized segments to synthesize long motion sequences. Across 100 motion styles on an SMPL humanoid, PhysibleMDM reduces mean ground penetration, self-collision penetration, and ground slip by 75%, 92%, and 74%, respectively, relative to unoptimized diffusion output. Across 11 sequences for a custom bipedal robot, it achieves median reductions of 89.5% in per-sequence mean acceleration-reconstruction error and 79.5% in the mean inverse-dynamics residual.
Figures & tables
Figure 1: Overview of PhysibleMDM. We improve physical feasibility by optimizing the diffusion noise of a frozen motion generator. Kinematic constraint violations and constrained inverse-dynamics residuals serve as physical-feasibility proxies, guiding refinement without simulator rollouts. Initial (purple) and optimized (blue) motions illustrate improvements in dynamic feasibility (top) and kinematic feasibility (bottom). Optimized motion history conditions subsequent generation.
Figure 2: Qualitative comparison of unoptimized motion (gray-purple) and Physible-optimized motion (cyan-blue). (a) Ground-contact behavior for the SMPL humanoid during the cat motion, with side-view foot trajectories and minimum foot clearance. (b) Arm self-collision behavior during the lawn-mower motion, with top-down arm trajectories and minimum arm-pair clearance. In both panels, negative clearance indicates penetration, and red collision geometries mark active collisions or penetrations. (c) Dynamic feasibility of the bipedal robot’s two-foot jump , with rendered snapshots, the translational acceleration residual norm, and planned (solid) versus feasible (dashed) vertical acceleration. Physible reduces the illustrated feasibility violations while preserving the characteristic motion patterns.
Method
Ground Penetr. [mm] ↓
Self-Coll. Penetr. [mm] ↓
Ground Slip [m/s] ↓
Velocity Tracking ↓
Motion Consistency ↓
LDJ ↑
Style Acc. [%] ↑
Style FID (Overall) ↓
Style FID (Per-Style) ↓
Comp. Time ↓ Iter. / Horizon [ms] / [s]
Unoptimized
2.66e+0 [6.21e+0]
1.93e-1 [0.00e+0]
1.85e-1 [4.25e-1]
7.70e-2 [1.10e-1]
2.71e-4 [6.92e-4]
-6.42 [-7.15]
96.03
7.52
16.16 [44.54]
N/A / 0.02
Motion GD
3.59e+0 [9.61e+0]
1.92e-2 [1.43e-2]
4.80e-2 [1.45e-1]
2.01e-2 [5.74e-2]
9.89e-5 [3.33e-4]
-8.63 [-9.39]
95.51
7.64
15.90 [41.06]
57 / 5.79
Motion Sep-CMA-ES
1.32e+0 [2.85e+0]
1.41e-1 [2.36e-1]
1.17e-1 [2.54e-1]
6.79e-2 [1.09e-1]
1.17e-3 [3.77e-3]
-9.97 [-10.35]
95.54
7.52
16.75 [51.88]
23 / 2.41
Guided Diffusion
1.52e+0 [3.38e+0]
1.59e-1 [0.00e+0]
1.44e-1 [3.97e-1]
6.48e-2 [9.90e-2]
2.65e-4 [6.85e-4]
-7.02 [-7.75]
96.33
7.57
16.20 [41.30]
64 / 0.65
Noise Best-of-N
2.03e+0 [5.00e+0]
1.49e-1 [0.00e+0]
1.34e-1 [3.21e-1]
7.19e-2 [1.03e-1]
2.46e-4 [6.35e-4]
-6.45 [-7.20]
95.83
7.88
16.99 [42.26]
40 / 3.79
Noise GD
2.80e+0 [2.39e+0]
6.84e-3 [0.00e+0]
1.27e-2 [4.89e-2]
7.86e-3 [2.33e-2]
3.44e-4 [1.07e-3]
-7.60 [-8.62]
15.41
82.27
274.81 [396.01]
105 / 10.78
Table 1: Kinematic feasibility on the SMPL humanoid. Metrics show mean [p90 for ↓ ; p10 for ↑ ], except Style Acc. and Overall FID (means only). NNS: no noise standardization. Green indicates better performance; bold marks means within 3% of the best.
Method
Ground Penetr. [mm] ↓
Self-Coll. Penetr. [mm] ↓
Ground Slip [m/s] ↓
Velocity Tracking ↓
Motion Consistency ↓
LDJ ↑
Unoptimized
0.56 [1.43]
1.25e-2 [0.00e+0]
8.45e-2 [1.68e-1]
0.07 [0.11]
2.70e-4 [9.95e-4]
-7.52 [-8.08]
Motion GD
1.09 [2.91]
5.85e-3 [0.00e+0]
2.20e-2 [4.89e-2]
0.03 [0.09]
6.85e-5 [1.83e-4]
-10.53 [-11.19]
Motion Sep-CMA-ES
0.25 [1.28]
9.99e-3 [0.00e+0]
3.80e-3 [8.74e-3]
0.04 [0.08]
2.34e-4 [8.73e-4]
-9.52 [-10.31]
Guided Diffusion
0.74 [1.42]
1.15e-2 [0.00e+0]
1.09e-1 [2.38e-1]
0.07 [0.10]
2.44e-4 [9.27e-4]
-8.35 [-9.29]
Noise Best-of-N
0.49 [1.30]
9.68e-3 [0.00e+0]
5.24e-2 [1.19e-1]
0.06 [0.10]
2.22e-4 [8.34e-4]
-7.55 [-8.12]
Noise GD
0.70 [1.53]
2.85e-3 [0.00e+0]
1.15e-1 [2.70e-1]
0.10 [0.18]
9.67e-4 [4.71e-3]
-8.00 [-8.51]
Table 2: Kinematic feasibility on the bipedal robot. Metrics show mean [p90 for ↓ ; p10 for ↑ ]. NNS: no noise standardization. Green indicates better performance; bold marks the best results.
Method
Acceleration Reconstruction ↓
Inverse Dynamics Residual ↓
LDJ ↑
Comp. Time ↓ Iter. / Horizon [s] / [s]
Unoptimized
0.454 [0.954]
8.44e+1 [1.87e+2]
-7.71 [-8.11]
N/A / < 1
Motion Sep-CMA-ES
0.032 [0.056]
7.34e+0 [1.29e+1]
-11.67 [-11.83]
1.66 / 4145
Guided Diffusion
19.163 [34.988]
1.86e+3 [3.32e+3]
-9.91 [-10.37]
17.65 / 141
Noise GD
0.013 [0.022]
1.94e+0 [4.57e+0]
-10.03 [-10.69]
5.93 / 14828
Noise ZeNO
0.289 [0.545]
7.51e+1 [1.39e+2]
-8.49 [-8.76]
1.50 / 3751
Physible (ours)
0.081 [0.174]
2.65e+1 [6.27e+1]
-8.51 [-8.83]
1.81 / 4515
Table 3: Dynamic feasibility for the bipedal robot during a two-foot jump. Metrics show mean [p90 for ↓ ; p10 for ↑ ]. Green indicates better performance; bold marks the best results.
Appendix figures & tables56 assets
Supplementary material from the paper’s appendix.
Appendix
Term
Kinematic
Dynamic
Objectives
Velocity tracking Jtrack
✓
✓
Autoregressive motion consistency Jcons
✓
✓
Equality constraints
Ground slip hslip
✓
✓
Acceleration reconstruction hacc
✗
✓
Appendix
Table 4: Objectives and constraints actively included in the optimization loss for the two feasibility optimization settings. A checkmark indicates a nonzero loss weight; terms without a checkmark may still be evaluated for reporting.
Method
Batched sampling passes
Additional evaluation structure
Unoptimized
1
Score generated batch
Motion GD
1
K motion updates and final scoring
Motion Sep-CMA-ES
1
K populations and final mean scoring
Guided Diffusion
1
Score/guide at each step; score final motion
Noise GD
K+1
Regenerate after final noise update
Sampling-based noise methods
K+1
Initial population, K populations
Appendix
Table 5: Number of full Motion Diffusion Model reverse-sampling passes per horizon, each over the inference batch. Each pass contains D batched denoiser evaluations. Numerical budgets are specified in Appendix F.3 . Motion-space objective evaluations require no additional denoiser calls.
Parameter
SMPL (kinematic)
bipedal robot (kinematic)
bipedal robot (dynamic)
P,F
10,20
15,30
15,30
Fkeep,Fov
15,5
25,5
25,5
K
100
100
2500
Npop
64
64
64
D
8
8
8
bsyl,bpst
1,−0.5
2.5,−1
1.5,−0.5
Appendix
Table 6: Default optimization hyperparameters and objective weights for each embodiment and feasibility optimization setting. Experiment-specific settings are given in the corresponding subsections. Zero weights mean that a term does not contribute to the optimized loss.
Name
Term ri,t
Weight wi
Motion tracking
Root position
1−∥ptH−p^tH∥22
1.0
Root orientation
1−∥ρ6(RtH)−ρ6(R^tH)∥22
1.0
Root linear velocity
1−∥vtH−v^tH∥22
1.0
Root angular velocity
1−∥ωtH−ω^tH∥22
1.0
Rigid-body positions
1−∑b∥pb,tH−p^b,tH∥22
1.0
Appendix
Table 7: Downstream RL reward. Regularization terms are nonnegative costs with negative weights.
Figure 3: Convergence of kinematic feasibility optimization methods for a single motion horizon and constant forward reference velocity on the SMPL humanoid with neutral walking style with velocity command vcmd=(1,0,0) .
Metric
Result
Pairwise root trajectory RMSE [m]
3.51×10−2
Pairwise root orientation difference [rad]
1.99×10−2
Pairwise joint angle difference [rad]
5.00×10−2
Pairwise body position distance [m]
2.46×10−2
Best weighted loss
3.81×10−1±3.24×10−3
Velocity tracking
3.78×10−2±3.41×10−4
Appendix
Table 8: Optimizer-seed sensitivity of Physible on the SMPL humanoid: ten seeds, 100 styles, and 150 frames per style, with identical velocity commands. Motion rows report average pairwise differences; objectives and constraints report mean ± sample standard deviation across seeds after averaging over styles. Alignment and metric definitions are given in Appendix F.4 .
Figure 4: Ablation of the contact pattern preservation loss for neutral walking on the SMPL humanoid. Columns compare unoptimized motion, ground penetration distance loss, and contact pattern preservation loss. (a) Matched foot close-ups at 1.03 and 5.97s , with minimum signed ground clearance. (b) Minimum clearance over 16 checked points; positive values indicate that all points are above ground, and the dashed line marks the −5mm penetration allowance. (c) Target and observed left/right foot contacts; a foot is in contact when any checked point has nonpositive separation. (d) Summary over 240 samples at 30Hz , reporting the fraction of frames without contact, mean penetration, and longest continuous contact loss.
Figure 5: Part 1 of the ablation study compares two constraints for limiting (excessive) ground penetration during kinematic feasibility optimization on the SMPL humanoid for the neutral motion style: the baseline ground penetration constraint versus the proposed contact pattern preservation constraint. For each contact point, the left column shows the ground separation distance of the median unoptimized motion, the center column shows the best motion optimized with the ground penetration constraint, and the right column shows the best motion optimized with the contact pattern preservation constraint. Red shaded intervals indicate excessive-contact periods where penetration exceeds the threshold (as used by the contact pattern preservation constraint), while yellow shaded intervals indicate phases where none of the robot’s contact points are in contact with the ground.
Figure 6: Part 2 of the ablation study compares two constraints for limiting (excessive) ground penetration during kinematic feasibility optimization on the SMPL humanoid for the neutral motion style: the baseline ground penetration constraint versus the proposed contact pattern preservation constraint. For each contact point, the left column shows the ground separation distance of the median unoptimized motion, the center column shows the best motion optimized with the ground penetration constraint, and the right column shows the best motion optimized with the contact pattern preservation constraint. Red shaded intervals indicate excessive-contact periods where penetration exceeds the threshold (as used by the contact pattern preservation constraint), while yellow shaded intervals indicate phases where none of the robot’s contact points are in contact with the ground.
Figure 7: Kinematic feasibility optimization methods comparison for neutral walking on the Skinned Multi-Person Linear humanoid. (a) Matched-time snapshots of unoptimized motion, Motion Sep-CMA-ES, Guided Diffusion, Noise GD, and Physible. (b) Minimum signed height across contact points; negative values indicate ground penetration, while positive values indicate that all contact points are above ground. (c) Contact slip violation, averaged over all contact points after contact masking and velocity-threshold subtraction. (d) Maximum self-collision overlap across evaluated body pairs. (e) Root-mean-square joint jerk on a logarithmic scale. Diagnostics cover the full 5s clip, with a shared scale within each row; gray bands mark snapshot times. Physible reduces penetration and slip while retaining jerk closer to the unoptimized motion, although some ground penetration remains.
Figure 8: Behavior comparison of the root motion for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character.
Figure 9: Behavior comparison of the joint motion for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character - part 1.
Figure 10: Behavior comparison of the joint motion for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character - part 2.
Figure 11: Behavior comparison of the joint motion for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character - part 3.
Figure 12: Behavior comparison of the joint motion for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character - part 4.
Figure 13: Behavior comparison of the root motion in the x-y plane with integrated velocity command-based reference for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character.
Figure 14: Behavior comparison of the positional root motion in the x-y plane with integrated velocity command-based reference for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character.
Figure 15: Behavior comparison of the ground separation for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character.
Figure 16: Behavior comparison of the ground slip velocity for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character. The full-opacity and markers denoted active contacts (i.e., with a semi-negative ground separation distance). The transparent lines denote the tangential velocities of the contact points when they are not in contact and separated from the ground.
Figure 17: Behavior comparison of the contact pattern preservation for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character. The soft green and warm tints visualize time periods where the respective contact point should be in contact and not in contact with the ground, based on the contact pattern identified via a majority vote using the height threshold (purple-dashed line) using a batch of diffused, unoptimized motions. The red-dashed lines denotes the maximum-allowed ground penetration - Part 1.
Figure 18: Behavior comparison of the contact pattern preservation for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character. The soft green and warm tints visualize time periods where the respective contact point should be in contact and not in contact with the ground, based on the contact pattern identified via a majority vote using the height threshold (purple-dashed line) using a batch of diffused, unoptimized motions. The red-dashed lines denote the maximum-allowed ground penetration - Part 2.
Figure 19: Behavior comparison of the self-collision penetration for the kinematic feasibility optimization for 150 time steps of the neutral walking style on the SMPL humanoid character.
Figure 20: Ground-contact behavior for the SMPL humanoid during the cat motion. The top row shows rendered snapshots at time instants with visible foot-ground interaction for the unoptimized gray-purple character and optimized cyan-blue character. The lower panels compare unoptimized and optimized motion with matching side-view contact trajectories in the x - z plane and grouped foot-body ground distances for the ankles and toes. Positive values indicate separation above the ground plane, while negative values indicate penetration below the ground plane. The optimized motion significantly reduces foot-ground penetration while preserving the overall motion style.
Figure 21: Arm self-collision behavior for the SMPL humanoid during a lawn-mower motion. The top row shows rendered snapshots at collision-relevant time instants for the unoptimized gray-purple character and optimized cyan-blue character. The lower panels compare unoptimized and optimized motion with matching top-down arm trajectory views and selected hand-arm collision distances. Red-shaded and red-bordered collision geometries and red trajectory markers emphasize time steps for which collisions for the respective bodies take place. Positive signed distances denote penetration, while negative values denote separation. The optimized motion reduces arm interpenetration while preserving the overall motion style.
Figure 22: Part 1 of the comparison of the unoptimized vs. optimized self-collision penetration distance when used as a constraint during the kinematic feasibility optimization for 150 time steps of the lawn mower walking style on the SMPL humanoid character. The penetration/separation distances are determined via an Separating Axis Theorem algorithm applied to pre-defined collision pairs for bodies approximated as cuboids along separate leaves of the kinematic tree.
Figure 23: Part 2 of the comparison of the unoptimized vs. optimized self-collision penetration distance when used as a constraint during the kinematic feasibility optimization for 150 time steps of the lawn mower walking style on the SMPL humanoid character. The penetration/separation distances are determined via an Separating Axis Theorem algorithm applied to pre-defined collision pairs for bodies approximated as cuboids along separate leaves of the kinematic tree.
Figure 24: Motion-style preservation after kinematic feasibility optimization with Physible on the Skinned Multi-Person Linear humanoid. (a) Selected, matched-time snapshots of the cat , cross-over , and duck-foot styles at 0.70s , 1.40s , and 2.10s , comparing unoptimized motion (left) with Physible (right). (b) Style classification accuracy over each full 8s clip, computed from 15 -frame sliding windows and averaged in 1s bins; vertical markers indicate snapshot times. Cat and duck-foot retain 100% accuracy, while cross-over exhibits a temporary decrease after optimization.
Sequence
Frames / Duration [s]
Acceleration reconstruction ↓
Inverse-dynamics residual ↓
LDJ ↑
Unoptimized
Physible
Unoptimized
Physible
Unoptimized
Physible
Flat-ground motion styles
Two-foot jump
250 / 5
0.454 [0.954]
0.081 [0.174]
84.40 [186.93]
26.48 [62.70]
-7.71 [-8.11]
-8.51 [-8.83]
Left hop
150 / 3
0.511 [0.721]
0.009 [0.014]
106.43 [167.33]
1.91 [3.19]
-8.57 [-8.96]
-8.83 [-9.42]
Bouncy right
150 / 3
0.505 [1.014]
0.161 [0.271]
74.11 [147.12]
54.61 [95.67]
-7.59 [-7.80]
-8.27 [-8.56]
Skip
150 / 3
0.800 [0.927]
0.059 [0.175]
93.73 [166.87]
19.20 [64.97]
-7.69 [-7.95]
-8.31 [-8.73]
Appendix
Table 9: Dynamical feasibility across bipedal-robot sequences. Each sequence is reported separately for Unoptimized and Physible. Entries are mean [p90] for acceleration reconstruction and inverse-dynamics residual, and mean [p10] for LDJ. Bold marks the better mean within each sequence and metric.
Metric
Result
Pairwise root trajectory RMSE [m]
7.57×10−2
Pairwise root orientation difference [rad]
4.38×10−2
Pairwise joint angle difference [rad]
1.38×10−1
Pairwise body position distance [m]
1.69×10−2
Acceleration reconstruction
8.77×10−2±9.79×10−3
Inverse-dynamics residual
28.82±3.38
Appendix
Table 10: Optimizer-seed sensitivity of Physible for two-foot-jump dynamic feasibility optimization on the bipedal robot: ten seeds and 150 frames ( 3s ) per seed, with identical velocity commands. Motion rows report average pairwise differences; evaluation metrics report mean ± sample standard deviation across seed-specific temporal means. Alignment and metric definitions are given in Appendix F.4 .
Figure 25: Comparison of dynamic feasibility optimization methods for the bipedal robot’s two-foot-jump motion: unoptimized generation, Motion Sep-CMA-ES, Guided Diffusion, Noise GD, and Physible. (a) Motion snapshots at the indicated times. The plots show (b) signed ground clearance, with negative values indicating ground penetration; (c) the absolute difference between planned and dynamically feasible vertical base acceleration, ∣Δaz∣ ; and (d) joint jerk over a 5s sequence. Gray vertical bands mark the snapshot times. The comparison illustrates trade-offs between acceleration consistency, ground contact, and motion smoothness: Noise GD has low acceleration error but remains above the ground, whereas Physible retains repeated ground contacts and the characteristic jumping motion.
Figure 26: Dynamical feasibility optimization of the two-foot-jump motion on the bipedal robot over a 2.5s horizon. The top row shows rendered video snapshots of the unoptimized and optimized motions, including the virtual root force visualization used during dynamical feasibility analysis. The second row shows the planned root trajectories from a side view: the unoptimized motion is rendered transparently in the background, while the optimized motion is rendered in the foreground. Robot configurations are shown at separate robot-pose times distributed across the full horizon, whereas the video snapshots correspond to the selected first-row rendering times. The gray vertical bands in the quantitative plots mark the video snapshot times, and the amber bands mark the robot-pose times used for the second-row configuration renderings. The translational and rotational acceleration residual plots visualize the planned root trajectory together with arrows denoting the residual acceleration, computed as planned minus dynamically feasible acceleration. Smaller residual arrows indicate improved dynamical consistency. The bottom rows compare planned and feasible root accelerations in the y - and z -directions; solid lines denote planned accelerations and dashed lines denote feasible accelerations, with separate colors for unoptimized and optimized motions.
Figure 27: Behavior comparison of the virtual wrench resulting from the relaxed Inverse Dynamics for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 28: Behavior comparison of the root acceleration residual for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 29: Behavior comparison of the root acceleration planned vs. feasible by method for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 30: Behavior comparison of the joint acceleration residual for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 31: Behavior comparison of the joint acceleration planned vs. feasible by method for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot – Part 1.
Figure 32: Behavior comparison of the joint acceleration planned vs. feasible by method for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot – Part 2.
Figure 33: Behavior comparison of the joint acceleration planned vs. feasible by method for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot – Part 3.
Figure 34: Behavior comparison of the tangential ground contact forces and the friction cone for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 35: Behavior comparison of the joint torques (including limits) for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot – Part 1.
Figure 36: Behavior comparison of the joint torques (including limits) for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot – Part 2.
Figure 37: Behavior comparison of the ground separation for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 38: Behavior comparison of the ground slip velocity for the dynamic feasibility optimization for 250 time steps of the two-foot-jump motion style on the bipedal robot.
Figure 39: Behavior comparison of the virtual wrench resulting from the relaxed Inverse Dynamics for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 40: Behavior comparison of the root acceleration residual for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 41: Behavior comparison of the root acceleration planned vs. feasible for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 42: Behavior comparison of the joint acceleration residual for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 43: Behavior comparison of the joint acceleration planned vs. feasible for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot - Part 1.
Figure 44: Behavior comparison of the joint acceleration planned vs. feasible for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot - Part 2.
Figure 45: Behavior comparison of the joint acceleration planned vs. feasible for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot - Part 3.
Figure 46: Behavior comparison of the tangential ground contact forces and the friction cone for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 47: Behavior comparison of the joint torques (including limits) for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot - Part 1.
Figure 48: Behavior comparison of the joint torques (including limits) for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot - Part 2.
Figure 49: Behavior comparison of the ground separation for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 50: Behavior comparison of the ground slip velocity for the dynamic feasibility optimization for 150 time steps of the left-hop walking style on the bipedal robot.
Figure 51: Dynamic feasibility optimization of the bipedal robot in the neutral style for (a) uphill ( +25∘ ) and (b) downhill ( −25∘ ) motion. Purple denotes unoptimized motion and blue denotes Physible. The snapshots show each pair at video timestamps 0.60 and 1.80s . All quantities use the slope-aligned frame with rotated gravity. From top to bottom, the plots show root pitch, along-slope and slope-normal accelerations (solid: planned; dashed: feasible reconstruction), and the norms of the linear and angular root acceleration residuals. Shading between acceleration curves highlights their mismatch. RMS annotations summarize each residual norm over the full sequence.
Diffusion models sample effectively from high-dimensional, multimodal distributions, but their outputs may violate deployment constraints. For task-space robot policies, generated grasps, waypoints, or trajectories can be distributionally valid yet infeasible, violating reachability, collision-avoidance, or closed-loop executability requirements. This embodiment gap limits zero-shot deployment across robots, even when the task-space behavior itself is transferable. We propose an inference-time optimization framework that couples the behavior generation to physical feasibility by formulating diffusion guidance as a constrained optimization problem. Our key insight is to replace the sampling perturbation in the backward process with an optimized correction, allowing hard constraints or soft penalties to be imposed during sampling without the need to retrain the diffusion model, while keeping samples close to the learned prior. We evaluate the method on dexterous grasp synthesis with reachability and collision-avoidance constraints, and dynamic manipulation with controller-level trackability constraints. Across settings and robot embodiments, optimization-guided denoising matches the feasibility of projection- and gradient-guidance baselines while better preserving grasp quality, and improving controller-level executability and task success, with task success improving by up to 20pp. on dexterous grasping and 23pp. on visuomotor manipulation over the best baseline.
Image-to-Video diffusion models leverage input images to generate visually stunning content, yet frequently produce motion that violates physical laws. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising; the phase degrades significantly (dropping by ≈18% from step 2 to step 50), whereas the magnitude remains relatively stable. Building on this insight, we propose PhaseLock, a training-free framework that preserves the valid motion priors from few-step inference throughout the denoising trajectory. Rather than relying on full-step inference for physical consistency, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. Our approach effectively mitigates phase degradation, improving physical consistency by an average of 6.2 points across diverse models while largely maintaining visual fidelity, with negligible overhead (1.06× time, 1.02× memory) and reduced reliance on expensive external guidance methods (∼5× time). Project Page: https://dnwjddl.github.io/phaselock
Woojung Han, Seil Kang, Youngjun Jun +3
1Yonsei University, South Korea · 2NVIDIA, Taiwan.
Recent progress in text-conditioned human motion generation has been largely driven by diffusion models trained on large-scale human motion data. Building on this progress, recent methods attempt to transfer such models for character animation and real robot control by applying a Whole-Body Controller (WBC) that converts diffusion-generated motions into executable trajectories. While WBC trajectories become compliant with physics, they may expose substantial deviations from original motion. To address this issue, we here propose PhysMoDPO, a Direct Preference Optimization framework. Unlike prior work that relies on hand-crafted physics-aware heuristics such as foot-sliding penalties, we integrate WBC into our training pipeline and optimize diffusion model such that the output of WBC becomes compliant both with physics and original text instructions. To train PhysMoDPO we deploy physics-based and task-specific rewards and use them to assign preference to synthesized trajectories. Our extensive experiments on text-to-motion and spatial control tasks demonstrate consistent improvements of PhysMoDPO in both physical realism and task-related metrics on simulated robots. Moreover, we demonstrate that PhysMoDPO results in significant improvements when applied to zero-shot motion transfer in simulation and for real-world deployment on a G1 humanoid robot.
Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI) · LIGM, École des Ponts, IP Paris, Univ Gustave Eiffel, CNRS · École polytechnique fédérale de Lausanne (EPFL)