Triangular Resampling for Long-Horizon Motion Generation

1 INTRODUCTION

• Training on short, ground-truth-derived windows mismatches inference states that repeatedly condition on model predictions, allowing errors to accumulate over long rollouts.The mismatch also occurs in partially denoised active-window states, which retain earlier predictions; replacing only completed history leaves it unresolved.Source: §1 · p. 2
• Triangular Resampling replays partially denoised states and uses a shared threshold to balance ground-truth anchoring with exposure to model predictions.States below the threshold are replaced with noise-matched ground truth after each update, while states at or above it retain predictions.Source: §1 · p. 2
• The replayed window supports supervised training and DMD-based distribution matching, yielding the TR and TR-DMD variants.Supervised TR uses paired clean-motion targets; TR-DMD combines triangular replay with the DMD update recipe.Source: §1 · p. 3
• 40.9% lower FID AUC than matched TR-off; TR and TR-DMD achieve state-of-the-art FID AUC within their respective comparison groups.The FID degradation slope falls from 0.526 to 0.235 per minute (55.3%) with TR versus TR-off.Source: §1 · p. 3

Long-Horizon Motion Generation

• Long-form motion methods compose segments, refine overlapping segments, or use positional encoding and latent composition; FloodDiffusion instead jointly denoises a bidirectional active window.TR optimizes FloodDiffusion’s training-state distribution rather than proposing another composition or sampling architecture.Source: §2 · p. 3

Rollout Training in Motion Generation

• Motion rollout methods expose models to predictions through history replacement or self-conditioned segment rollouts, whereas this work targets committed outputs and partially denoised tokens together.DART uses a staged history curriculum, MotionStreamer progressively replaces history tokens, and PRISM v1 applies Self Forcing to generated segments [Zhao et al., 2025; Xiao et al., 2025; Ling et al., 2026].Source: §2 · p. 3

Rollout Training in Video Generation

• Video-generation approaches include self-rollouts, recomputed historical representations, staggered rolling windows, and autoregressive-teacher initialization followed by DMD [Huang et al., 2025; Zhuang et al., 2026; Liu et al., 2026; Zhu et al., 2026].Resampling Forcing resamples corrupted ground-truth frames with the current model, while supervised TR uses detached generated states, retains ground-truth supervision, and applies one shared threshold throughout triangular replay [Guo et al., 2025].Source: §2 · pp. 3–4

3 PRELIMINARIES: FLOODDIFFUSION TRIANGULAR DENOISING

• The triangular schedule partitions positions into a clean prefix, an active denoising window, and a noisy suffix as global phase advances.The boundaries are m(τ) = ⌈(τ −1)c⌉ and n(τ) = ⌈τc⌉; c controls the slope and the number of simultaneously active tokens.Source: §3 · p. 4
• At inference, the Euler solver advances the global denoising phase in increments of 1/N, with each latent’s clean-data coefficient evaluated at the current phase.In the reported configuration, c = 5 and N = 10, so one token is committed every two Euler steps after the initial warm-up.Source: §3 · p. 4
• A bidirectional denoiser predicts velocities for active tokens, and Euler updates advance each position according to its change in denoising level.Source: §3 · p. 4
• When the leading token becomes clean, it is committed, the window shifts, and fresh noise enters at the trailing edge, enabling generation beyond the training sequence length.The active window remains bounded as this cycle repeats.Source: §3 · p. 4

4 TRIANGULAR RESAMPLING

• TR replays both completed history and partially denoised active-window states, using ground-truth clamping to control their exposure to model errors.This addresses the mismatch between ground-truth-derived training windows and model-generated inference states.Source: §4 · p. 4

4.1 GT-CLAMPED TRIANGULAR ROLLOUT

• A replayed sample resets a bounded interval to Gaussian noise, then follows triangular Euler updates, commits, shifts, and fresh-noise injections until its sampled training phase.Any earlier prefix stays clean, and the resulting replay state is detached before optimization.Source: §4.1 · p. 5
• One shared threshold controls release: below it, tokens use noise-matched ground truth; at or above it, they retain model predictions.The shift s controls clamp strength: smaller s favors earlier release, while larger s retains ground-truth anchoring longer.Source: §4.1 · p. 5

4.2 OPTIMIZATION OBJECTIVES

• Supervised TR trains on replayed states that retain model-induced errors, applying clean-motion supervision to the output band while the remaining window provides context.For model-generated states, the objective uses a velocity toward the paired clean latent; samples that bypass replay use the ordinary FloodDiffusion objective.Source: §4.2 · p. 5
• TR-DMD retains triangular replay and ground-truth clamping but uses distribution matching on clean predictions recomputed at a sampled denoising stage.Its update follows Rolling Forcing’s DMD recipe, using frozen real-score and trainable fake-score models.Source: §4.2 · p. 6

5.1 EXPERIMENTAL SETTINGS

• Evaluation uses 120-second sequences from HumanML3D test prompts, split into twelve 10-second windows tracking FID, Matching Distance, and R-precision.Source: §5.1 · p. 6

5.2 MAIN RESULTS

• Against matched TR-off, TR reduces FID AUC from 1.951 to 1.153 (40.9%) and FID degradation slope from 0.526 to 0.235 per minute.Source: §5.2 · p. 7
• Table 1 places TR at FID AUC 1.153 in the non-DMD group and TR-DMD at 1.324 in the DMD group, each best in its group.Source: Table 1 · p. 7, §5.2 · p. 7

5.3 ABLATION STUDY

• Full self-rollout reaches FID AUC 16.024 versus 1.251 at s = 0.6; random-position clamping and curriculum yield 1.857 and 1.455, respectively.Source: §5.3 · pp. 8–9
• The shift sweep favors s = 0.6: FID AUC is 2.044 at s = 0.3, 1.349 at s = 3, and at least 2.765 for s ≥ 100.Source: §5.3 · p. 8
• Replay ratios show a non-monotonic FID AUC pattern: γ = 0.25 and γ = 1 yield 1.153 and 1.251, both below γ = 0.5 at 1.495.Source: §5.3 · p. 9

5.4 HUMAN EVALUATION

• In blinded pairwise video evaluation on 30 prompts, TR has the highest BT scores for motion quality (0.302) and text alignment (0.317).Source: Table 3 · p. 9, §5.4 · p. 9

• TR replays active-window trajectories, including partially denoised states, and uses ground-truth clamping to control their release into model rollouts.Source: §6 · p. 9
• Supervised TR reduces FID AUC by 40.9% relative to matched TR-off, and TR and TR-DMD achieve the lowest mean FID AUC in their respective groups.Source: §6 · p. 9
• Multi-step replay increases post-training cost; initial 5k-update shared-GPU runs took about 1.95 seconds per TR update versus 0.58 seconds for TR-off.Source: §6 · p. 9

• Existing motion datasets and pretrained models are used under their respective licenses and access terms.Source: ETHICS STATEMENT · p. 10
• Human evaluation is voluntary, based on informed consent, and allows participants to withdraw at any time.Source: ETHICS STATEMENT · p. 10
• Participants receive compensation above the local average hourly wage; responses are de-identified and used only for research.Source: ETHICS STATEMENT · p. 10

• Equations 1–10 specify the schedule, replay, clamp distribution, supervised target, and differentiable DMD readout.Source: REPRODUCIBILITY STATEMENT · p. 10
• Section 5 records evaluation horizon and windowing, update budgets, initialization, and the ablation grid; Appendix B records external-method protocols.Source: REPRODUCIBILITY STATEMENT · p. 10
• The authors state that they will publicly release implementation, configurations, frozen prompt manifests, checkpoint identifiers, and evaluation scripts.Source: REPRODUCIBILITY STATEMENT · p. 10

AI USE STATEMENT

• AI tools assisted literature discovery, experiment planning, implementation, and manuscript drafting; the authors reviewed the work and take responsibility for the final content.The statement also notes that the authors reviewed cited sources, technical descriptions, and code behavior.Source: AI USE STATEMENT · p. 10

A TR AND TR-DMD IMPLEMENTATION DETAILS

• Supervised TR uses (γ, s) = (0.25, 0.6) with contiguous-frontier clamping, selected from the reported ratio sweep rather than a held-out set.This was the lowest-FID-AUC configuration in the reported sweep.Source: A TR AND TR-DMD IMPLEMENTATION DETAILS · p. 12
• TR-DMD uses effective batch size 64, separate generator and fake-score learning rates, and the final 1,200-iteration checkpoint.The total budget includes the preceding 30k supervised updates, and both scores load the same 10k-update motion-teacher EMA.Source: A TR AND TR-DMD IMPLEMENTATION DETAILS · p. 12
• DMD scoring networks evaluate at most the final 35 latents; cropped sequences use causal-VAE boundary re-encoding, while shorter ones retain valid lengths.Source: A TR AND TR-DMD IMPLEMENTATION DETAILS · p. 12

• All comparison models use HumanML3D+BABEL data, frozen prompts, duration, frame rate, reference bank, and evaluator weights, while objectives and several training choices remain method-specific.Metrics are computed independently within each repeat, and external systems are adapted to 263-dimensional motion using released code.Source: B EXTERNAL-METHOD TRAINING AND… · p. 13
• TR-off is matched post-training without triangular replay; Gaussian history noise instead perturbs conditioning history while leaving the supervised band unchanged.Both comparisons use matched initialization, data, and updates; Gaussian history noise is a baseline comparison, not a TR ablation.Source: B EXTERNAL-METHOD TRAINING AND… · p. 13
• External adaptations use fixed budgets and method-specific initialization stages; the Causal Forcing protocol is the authors’ released long-video extension, not a requirement of that method.The stated budgets are not claims of convergence at the original video scale.Source: B EXTERNAL-METHOD TRAINING AND… · p. 13
• An iteration means an outer DMD iteration, and NFE counts denoising evaluations per method-specific committed unit.The adaptations use five-latent blocks, unlike the video implementations’ three-latent blocks; selected methods use predeclared final checkpoints.Source: B EXTERNAL-METHOD TRAINING AND… · p. 13
• Table B1 records training and inference protocols for external 263-dimensional adaptations, including AR, ODE, DMD stages and NFE per committed unit.Source: Table B1 · p. 13

• Thirty prompts were selected by text review for sustained motion, excluding one-shot or finite actions; each method generated one 120-second motion per prompt.The set spans locomotion, running, dance, repetitive exercise, and gestures or ground motion; Table C1 lists the prompts verbatim.Source: C PAIRWISE PREFERENCE EVALUATION… · p. 14, Table C1 · p. 15
• All 90 videos use a consistent renderer and synchronized 120-second pair presentation, with prompts and playback time but no method labels.A red trail retains the ground-plane root trajectory, and Figure C1 shows a frame captured at 60 seconds.Source: C PAIRWISE PREFERENCE EVALUATION… · p. 14, Figure C1 · p. 14
• Each prompt contributes three method-pair comparisons across three rounds, with left-right order varied and method identities hidden.The same videos are assessed in all rounds, yielding 270 comparisons.Source: C PAIRWISE PREFERENCE EVALUATION… · p. 14
• Annotators make separate forced A/B choices for overall motion quality and text alignment, with no numerical rating or tie option.Quality concerns coherent movement; alignment concerns sustained adherence to the instruction.Source: C PAIRWISE PREFERENCE EVALUATION… · pp. 14–15
• Bradley–Terry models are fit separately by criterion to pooled judgments; higher fitted log-strength indicates stronger joint preference, not pairwise win percentage.The fit pools 270 judgments per criterion across three rounds rather than averaging round-wise scores.Source: C PAIRWISE PREFERENCE EVALUATION… · p. 15