Optimizing Diffusion Noise Can Serve As Universal Motion Priors

• Many motion tasks share the form of finding plausible motions that satisfy criteria, but a versatile framework for using motion priors expressively is lacking.Examples include trajectory and joint targets, obstacle avoidance, denoising, completion, and editing.Source: §1 · p. 2
• Earlier approaches use diffusion models for specific controls or task-based objectives, but face limits in generality or in control fidelity and motion quality.The discussion identifies scene perception for arbitrary or changing obstacles as one challenge for control-based approaches.Source: §1 · p. 2
• DNO back-propagates gradients through the full diffusion denoising process to optimize latent noise according to user-provided motion-space criteria.The method treats denoising as a black box and frames motion tasks as optimization on the diffusion model's latent manifold.Source: §1 · p. 2
• Without model fine-tuning, DNO produces high-quality edited motions, outperforming existing methods in preserving content and fulfilling objectives such as trajectory, pose, joint-location, and obstacle constraints.It also produces smooth and realistic motion from noisy and partial inputs.Source: §1 · p. 2

• Motion editing under the synthesis framework remains unexplored because existing approaches lack an explicit mechanism to retain original motion content.Source: §2 · p. 2
• Sparse-tracking models such as EgoEgo, AGRoL, and AvatarPoser are specialized for completion or denoising, leaving their priors' use on other tasks unclear.Source: §2 · pp. 2–3
• DNO uses trained motion diffusion models in a unified framework for editing, completion, and refinement rather than relying on specialized models for individual tasks.Source: §2 · p. 3
• Inspired by DOODL's latent optimization for image editing, DNO uses an improved optimization algorithm and does not require an invertible ODE.The paper presents this as making DNO simpler and convenient to use.Source: §2 · p. 3

3.1. Motion generation with diffusion model

• A diffusion probabilistic model learns to reverse a noising process by predicting denoising steps conditioned on inputs such as text prompts.Source: §3.1 · p. 3
• Deterministic sampling can use a probability-flow ODE or DDIM formulation, with an ODE solver generating a sample from Gaussian noise.Source: §3.1 · p. 3

3.2. Diffusion model inversion

• Diffusion inversion retrieves the noise map corresponding to an input motion by solving the deterministic sampling ODE backward, though fidelity depends on a smoothness assumption.Source: §3.2 · p. 3

3.3. Motion representation

• The relative-root representation stores 263 joint features per frame in a D × M matrix and abstracts away absolute root location.Its abstraction can improve generalization but makes controllable generation more challenging.Source: §3.3 · p. 3

4. Diffusion Noise Optimization

• Latent-space optimization keeps decoded motions on an expressive motion manifold, avoiding direct optimization in motion space where most representations are implausible.For diffusion models, the chosen latent is the noise at time T, xT.Source: §4 · p. 3
• DNO varies the task-specific criterion while keeping the pretrained motion model intact, enabling different motion tasks through changes to the loss.The method uses the DDIM-ODE and its solver.Source: §4 · p. 4
• DNO optimizes diffusion noise by evaluating a task loss on the generated motion and backpropagating its gradient through the full ODE denoising process.The optimized noise is decoded once more to produce the final motion.Source: §4 · p. 4
• Backpropagating through the ODE solver can be memory-intensive; gradient checkpointing or an invertible ODE can address this at added computation or model complexity.The authors note that few ODE function evaluations can make the memory overhead feasible in the motion domain.Source: §4 · p. 4
• Unlike guided diffusion methods [33], DNO computes the criterion on the fully denoised motion, avoiding the approximation error from evaluating an expected clean motion at an intermediate step.The guided-method criterion approximates the expected loss using the expected clean motion, which can incur severe error when the conditional variance is large.Source: §4 · p. 4

5. Applications

• DNO frames conditional motion synthesis applications around task-specific criteria and auxiliary losses, with noise initialization selected for the task.Motion refinement and completion cover noisy or incomplete inputs, including missing frames or joints and motion blending.Source: §5 · pp. 4–5, §5.2 · p. 5

5.1. Motion editing and control

• Motion editing combines target-joint and keyframe location losses with obstacle-avoidance losses, while reference-noise initialization and a noise-distance penalty help preserve the original motion.Obstacle losses use signed distance fields with a safe-distance threshold; targets can cover selected joints and frames.Source: §5.1 · p. 5

5.2. Motion refinement and completion

• Motion refinement starts from random noise and matches all observed joints to the noisy input, while a multiscale latent-decorrelation loss can be combined with the pose loss.The authors report that decorrelating latent dimensions alleviates foot skating; successive average pooling provides the temporal scales.Source: §5.2 · p. 5
• Motion completion also starts from random noise, but matches only the existing input joints so the optimization can fill in missing information.The input may itself be noisy.Source: §5.2 · p. 5

6. Experiments

• Experiments use HumanML3D when applicable; editing tests use six inputs and 96 outputs, while refinement tests use 300 motions with 5-cm noise or incomplete, noisy joint inputs.Editing optimization runs for 300 steps; refinement runs for 500 steps.Source: §6 · p. 6, §6.1 · p. 6, §6.2 · p. 7

6.1. Motion Editing

• DNO outperforms GMD across all tested editing actions and metrics except Foot skating ratio for “crawling,” with lower Jitter, higher content preservation, and low objective errors.Table 1 evaluates actions generated from MDM prompts and computes content preservation against the input motions.Source: Table 1 · p. 6, §6.1 · pp. 6–7

6.2. Motion Refinement

• Across noisy-refinement experiments, DNO reduces MPJPE beyond the input level and produces smooth, realistic motions.The 5-cm-noise results use a subset of HumanML3D with N = 300.Source: Table 2 · p. 7, §6.2 · p. 7
• DNO-GMD outperforms DNO-MLD, DNO-MDM, and HuMoR, while every DNO combination outperforms GMD on motion refinement.The three paired diffusion models are ordered MDM, MLD, and GMD from higher to lower motion-generation FID.Source: §6.2 · p. 7

6.3. Ablation studies

• Normalized gradients reduce MPJPE, corresponding to lower Lpose, from 30.2 to 8.7 cm in the 1-cm-noise refinement ablation.The authors report that iterative diffusion-model calls can produce gradient norms spanning multiple orders of magnitude.Source: §6.3 · p. 8
• Decorrelating latent noise improves Foot skating ratio from 0.10 to 0.07 and Jitter from 0.40 to 0.33, but raises MPJPE from 6.8 to 8.7.The decorrelation loss discourages correlations across the time axis in xT.Source: §6.3 · p. 8
• DDIM 5, 10, and 20 steps yield MPJPE scores of 9.8, 8.7, and 7.9; tested random perturbations worsen FID, and γ = 10^-3 harms optimization.The authors choose 10-step sampling as a balance between result quality and resource use.Source: §6.3 · p. 8

7. Discussion and Limitations

• DNO works better when observations cover more of the body, and its effectiveness is limited by the underlying diffusion model.The authors also note that some cases resist projection to realistic motion and that optimization speed limits interactive editing.Source: §7 · p. 8
• DNO is a plug-and-play motion prior that supports editing and other motion tasks without training a new model for each task.The authors describe it as enabling precise, fine-grained control for motion editing.Source: §7 · p. 8

A. Motion completion

• Motion completion generates full-body motion from partial joint observations, using ground-truth joint locations without added noise.Table A.1 reports results on a subset of HumanML3D; experiments use N = 300 except DNO-MLD*, which uses 1,000 optimization steps.Source: A. Motion completion · p. 13, Table A.1 · p. 13
• DNO-GMD outperforms other baselines on MPJPE and FID, while HuMoR tends to produce smoother motions.The completion results are consistent with the motion denoising experiment.Source: A. Motion completion · p. 13

B. Additional motion-related tasks

• The same DNO method can be adapted to motion blending and in-betweening without retraining the model.Qualitative results are provided in the supplementary video.Source: B. Additional motion-related tasks · p. 13

B.1. Motion Blending.

• Motion blending optimizes from random noise toward concatenated input-motion joint targets, leaving a 10-frame transition window unconstrained for the motion prior to fill.The transition window is centered on the concatenation; the task uses λ_cont = 0.0, λ_decorr = 10^3, γ = 0, and 1,000 optimization steps.Source: §B.1 · p. 13

B.2. Motion In-betweening.

• Motion in-betweening generates motion between given starting and ending poses by optimizing against partial-observation joint targets.It uses the motion-blending setting, differing only in the number of target joints.Source: §B.2 · p. 13

C. Why we do not report FID for motion editing.

• FID is not meaningful for motion editing because only one pre-edit sequence and a few post-edit sequences are available.The metric measures differences between distributions and requires many samples in both datasets.Source: C. Why we do not report FID for motion… · p. 13

D. GMD implementation details

• The GMD comparison uses Emphasis projection and Dense gradient propagation for all tasks, omits the trajectory model, and applies the same criterion terms as DNO.For ground-location conditioning, it uses GMD's point-to-point imputing method until t = 20.Source: D. GMD implementation details · p. 13
• Because GMD does not support editing while preserving content, the editing comparison supplies both the text prompt and target condition.Noisy refinement and completion instead use observed joints without text conditioning.Source: D. GMD implementation details · pp. 13–14

E. HuMoR implementation details

• HuMoR evaluations use both pose and motion priors; its model was trained on 30-FPS AMASS data that does not fully overlap with 20-FPS HumanML3D sequences.HuMoR interpolates to match the input frame rate, and sequences with failed optimizations are excluded from its metrics.Source: E. HuMoR implementation details · p. 14

F. SDEdit on motion refinement

• SDEdit fails to preserve original content across tested settings, and all settings except t = 1000 produce unrealistic motions affected by input noise.At t = 1000, it becomes a standard DDPM process with no content preservation; the reported FID is 29.73 because unprompted MDM motions are biased toward simple actions such as standing.Source: Table F.1 · p. 14, F. SDEdit on motion refinement · p. 14

F.1. Qualitative Results

• Supplementary video provides qualitative DNO results for editing, refinement, blending, and in-betweening.Source: §F.1 · p. 14

G. Differences from guided diffusion method

• DNO optimizes a latent code with a full-chain diffusion sample at each step, while LGD steers one sampling trajectory and outputs a guided sample.DNO's output is a latent code whose decoded sample follows the guidance; LGD directly outputs a sample following guidance.Source: G. Differences from guided diffusion… · p. 14
• DNO evaluates the loss on the exact full-chain output, whereas LGD uses an approximate expected motion whose error is severe at high conditional variance.The passage locates high variance particularly near the beginning of denoising, when T is about 1000.Source: G. Differences from guided diffusion… · p. 14
• 25.7 vs 9.1 MPJPE: GMD reaches targets less well than DNO in the reported comparison.The passage attributes the difference to approximation error in LGD guidance.Source: G. Differences from guided diffusion… · p. 14
• DNO can optimize latent noise to find a valid motion close to a noisy input, while GMD is ineffective on the reported refinement task.The paper describes the latent space as a prior for valid motions.Source: G. Differences from guided diffusion… · p. 14
• LGD's conditional-sampling approach makes it unclear how to specify which input aspects to preserve, while DNO supports minimal latent updates for content-preserving edits.Nearby latent codes are likely to produce nearby motions; experiments also report DNO tasks requiring precise control, motion priors, or content preservation that LGD cannot effectively solve.Source: G. Differences from guided diffusion… · pp. 14–15