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TACD: Distilling Efficient Text-to-Motion Models via Terminal Amplification Control

Wei-Jin Huang, Yuan-Ming Li, Kun-Yu Lin, Wang Luo, Yinlin Zhu, Yue Yu, Shenghao Ye, Junbin Yuan, Fa-Ting Hong, Qing Zhang, Wei-Shi Zheng

arXiv:2610.02867v1cs.AI

TL;DR

Text-to-motion models can be slow and memory-intensive because they require repeated evaluations of large models, while real-motion training data may be unavailable. TACD bounds supervision weights during on-policy distillation, and its few-step students improve over truncated teachers while compact students reduce inference costs.

  • Problem

    Text-to-motion generation remains difficult to deploy promptly within limited device memory, and real-motion examples may be unavailable when adapting released generators.

    Source: §1 · p. 2

  • Method

    TACD trains students from text prompts and pretrained teachers, using clean-motion predictions along student-generated trajectories and a step-size-aware bound on supervision weights.

    Source: §1.041 · p. 2, §3 · p. 3

  • Results

    Few-step TACD students improve over teachers truncated to their step count; eight-step HY-Motion student FID falls 58% versus uncapped distillation.

    Source: §1.041 · p. 3, §4.3 · p. 9

  • Takeaways & Limitations

    Eight-step students with compact components run 7.7–11.9× faster end to end and use 3.8–6.7× less peak GPU memory than their teachers.

    Source: §1.041 · p. 3

Abstract

from arXiv · show

Recent text-to-motion models have improved motion quality and instruction following, yet many-step denoising and large model components make deployment slow and memory-intensive. We present Terminal-Amplification-Controlled Distillation (TACD), an on-policy approach for training efficient motion generators from text prompts and pretrained teachers, without real-motion training data. Building on segmented on-policy flow distillation, we supervise clean-motion predictions along student-generated trajectories. We identify a failure mode in which velocity matching on a fixed supervision grid repeatedly overweights errors near the denoising endpoint, degrading few-step generation. TACD ties the latest teacher query to the student's step size, bounding the effective loss weights in clean-motion space without changing inference. Experiments on HumanML3D and KIT-ML demonstrate improved few-step generation, including a 58% reduction in eight-step HY-Motion student FID relative to distillation without this bound. For diffusion teachers, the endpoint-matching form of TACD yields four-step students with lower FID and matched or improved text-motion retrieval relative to their 50-step teachers on HumanML3D. On HY-Motion and Kimodo, eight-step students with compact components achieve 7.7-11.9x end-to-end speedups and reduce peak GPU memory by 3.8-6.7x relative to their teachers. Project page: https://vkgo.github.io/TACD/

1 INTRODUCTION

Text-to-motion models are difficult to deploy when repeated evaluations of large models strain latency and memory, while motion data may be unavailable for distillation. TACD bounds supervision weights in on-policy distillation; experiments report improved few-step results and more efficient students.

1 INTRODUCTION

  • Few-step generation alone does not shrink the motion backbone or conditioning encoder, and real-motion examples may be unavailable when adapting a released generator.Source: §1 · p. 2
  • On a fixed supervision grid, velocity matching repeatedly overweights errors near the denoising endpoint, and controlled interventions show that bounding this weight restores few-step quality.Source: §1 · p. 2, Figure 2 · p. 2

1.041 TACD

  • TACD ties the latest teacher query to the student’s step size, bounding supervision weights while retaining on-policy teacher targets along student-generated trajectories.The method also extends to diffusion teachers through endpoint matching.Source: §1.041 · p. 2
  • On HumanML3D, eight-step HY-Motion student FID falls from 2.486 to 1.041; compact students run 7.7–11.9× faster and use 3.8–6.7× less peak GPU memory than teachers.The efficiency results are reported for HY-Motion and Kimodo students.Source: §1.041 · pp. 2–3
  • Four-step endpoint-matching students of two diffusion teachers match or improve their teachers on FID and text–motion retrieval on HumanML3D.Source: §1.041 · p. 2

2 RELATED WORK

Prior motion-generation work spans diverse model families and acceleration strategies; TACD is positioned at the intersection of on-policy flow distillation and prediction–loss alignment.

Efficient and data-free motion distillation

  • Text-to-motion acceleration spans several generator families and distillation strategies, while MotionLCM (Dai et al., 2024b) uses real motions and this work adopts teacher-output supervision without real-motion targets.Solver and compression methods address complementary inference costs.Source: §2 · p. 3

Policy-based generative distillation

  • π-Flow (Chen et al., 2026) builds a queryable DX velocity policy from predicted clean samples; this work uses its single-knot specialization and focuses on endpoint parameterization over a few-step supervision grid.Other on-policy work studies arbitrary-interval flow maps, flow-matching distillation, or black-box adversarial transfer.Source: §2 · p. 3

Prediction–loss alignment and temporal supervision

  • Prior work studies prediction parameterizations and induced loss weights; on a fixed grid, recurring near-terminal supervision becomes a fixed coefficient, motivating a step-size-tied bound.Related analyses include Hong et al. (2026) on inverse-square endpoint-to-velocity amplification, JiT (Li & He, 2025) on clipping the conversion denominator, and FlowCTS (Ye et al., 2026) on transition-kernel KL weighting.Source: §2 · p. 3

3 METHOD

TACD trains clean-motion predictions on frozen-teacher targets from student-generated trajectories, then controls how strongly each supervision query contributes. It bounds terminal weights without changing the inference schedule, and extends endpoint matching to diffusion teachers.

3.1 SEGMENTED ON-POLICY DISTILLATION

  • The student predicts the complete clean motion once at each segment start, and a frozen teacher supplies targets on detached states along the student-generated rollout.Teacher targets and rollout states are constants for the update, so gradients pass only through online predictions at segment starts.Source: §3 · p. 3, §3.1 · pp. 4–5

3 METHOD

  • TACD is a supervision design for segmented on-policy distillation that regulates weights induced by velocity matching and extends endpoint matching to diffusion teachers.The student predicts clean motion while teacher queries provide training targets along its generated trajectory.Source: §3 · pp. 3–4

3.2 TERMINAL AMPLIFICATION IN VELOCITY MATCHING

  • On a fixed supervision grid, the final query receives coefficient δ^-2; with δ = 10^-3, it is 10^6, and this same near-terminal weight recurs every update.A large coefficient alone does not establish that its term dominates the update; gradient share also depends on the residual and student Jacobian.Source: §3.2 · p. 5

3.3 TERMINAL AMPLIFICATION CONTROL

  • TACD bounds supervision weights by tying the latest teacher query to the student’s step size, without changing the inference update or adding a network module.For flow teachers, its grid-capping rule moves final-segment queries while retaining velocity matching.Source: §3 · pp. 3–4, §3.3 · p. 5

3.4 EXTENSION TO DIFFUSION TEACHERS

  • For diffusion teachers, endpoint matching compares clean-motion estimates directly, removing time-dependent weights while training on deterministic DDIM rollout states.This form of TACD uses frozen-teacher targets at detached student-rollout states.Source: §3.4 · p. 6

4 EXPERIMENTS

Across flow and diffusion teachers, TACD improves few-step motion quality; controlled interventions link the flow gain to bounding terminal supervision weights. Evaluations also report same-step gains on KIT-ML and Kimodo and deployment savings on HY-Motion and Kimodo.

4.1 EXPERIMENTAL SETUP

  • Experiments use teacher supervision and training-split captions as text, without real-motion targets, across HY-Motion, diffusion teachers, KIT-ML, and Kimodo.The HY-Motion flow student uses eight-step inference; diffusion students are evaluated at two, four, and eight steps.Source: §4.1 · p. 6, §4 · p. 6

4.2 FEW-STEP MOTION QUALITY

  • At eight steps on HumanML3D, TACD reduces mean FID from 2.486 to 1.041 and improves R@3 from .708 to .782.TACD is best in R@1, R@3, MM-Dist, and FID at this budget.Source: §4.2 · p. 7, Table 1 · p. 7

4.3 SUPERVISION ANALYSIS AND CONTROLLED INTERVENTIONS

  • Moving only the final query from .999 to .9375 yields FID 1.039 versus 1.041 with full capping; gradient concentration follows the grid, and restoring C = 106 raises FID to 2.669.The controlled intervention improves FID in all three seeds.Source: §4.3 · pp. 7–8

4.4 OTHER TEACHERS AND DATASETS

  • On HumanML3D, four-step diffusion TACD improves teacher FID and retrieval; on KIT-ML and Kimodo, TACD beats same-step truncated teachers.For MLD and MotionLCM-V2 diffusion teachers, the four-step FID results are .222 versus .387 and .055 versus .066, respectively.Source: §4.4 · p. 9, Table 6

4.5 QUALITY–EFFICIENCY TRADE-OFFS

  • Eight-step HY-Motion TACD reduces peak GPU memory from 17.63 to 2.62 GB and end-to-end time from 2077 to 268 ms; Kimodo TACD is 11.9× faster with 3.8× lower peak memory.Measurements use an RTX L40 at batch 1 for HY-Motion; the Kimodo student uses a trained-in 1B encoder.Source: §4.5 · p. 9

5 CONCLUSION

TACD trains text-to-motion students from text prompts and pretrained teachers without real-motion training data. It controls fixed-grid terminal over-weighting and uses compact encoders and backbones to reduce latency and memory.

5 CONCLUSION

  • TACD trains efficient text-to-motion students from text prompts and pretrained teachers alone, without real-motion training targets.The method uses on-policy distillation.Source: §5 · p. 10
  • On a fixed supervision grid, velocity matching repeatedly overweights the near-terminal query; bounding that weight restores few-step quality.TACD ties the latest teacher query to the student's step size.Source: §5 · p. 10
  • Compact encoders and backbones reduce deployment latency and memory.Source: §5 · p. 10

SUPPLEMENTARY MATERIAL

The appendix expands Section 3 with training objectives, implementation conventions, and the diffusion-teacher branch. It specifies rollout predictions, gradient conversion, endpoint matching, and coefficient interventions.

A OBJECTIVE AND IMPLEMENTATION DETAILS

A.1 OBJECTIVE DEFINITIONS

  • The objective definitions introduce, in order, the rollout prediction, conversion-factor gradient, and two experimental loss variants.Source: §A.1 · p. 15
  • The EMA student predicts clean motion at each rollout segment start without gradient; that prediction fixes the next segment start and supervision states.Source: §A.1 · p. 15
  • Because supervision states and teacher targets are detached, the conversion factor does not depend on student parameters, and the gradient conversion holds query by query.Each query's gradient is scaled by (1 − t)^−2.Source: §A.1 · p. 15
  • Endpoint matching compares student clean-motion predictions directly with teacher clean-motion estimates at supervision states, and is TACD's diffusion-teacher form.Source: §A.1 · p. 15
  • Coefficient interventions alter one query's velocity-loss weight; its endpoint-equivalent coefficient is a_k,j(1 − s_k,j)^2, and terminal weight capping uses C = 4K^2.Source: §A.1 · p. 15

A.2 TRAINING ALGORITHM AND CONVENTIONS

The appendix documents the flow training iteration and conventions, the diffusion-teacher branch, and the shared experimental settings. It specifies fixed supervision times, detached rollout states, and the objectives used for flow and diffusion.

A.2 TRAINING ALGORITHM AND CONVENTIONS

  • Training uses M = 2 deterministic supervision points per segment on a fixed grid, with randomness only from noise and the prompt.Source: §A.2 · p. 15
  • The flow residual is an endpoint residual implicitly weighted by (1 − t)^−2; endpoint matching removes that factor on the same states.The last segment excludes its upper endpoint by margin δ because the velocity expression is singular as t approaches 1.Source: §A.2 · pp. 15–16
  • The rollout EMA supplies detached segment starts and supervision states, the frozen teacher supplies targets, and gradients pass only through online segment-start endpoints.Source: §A.2 · p. 16

A.3 DIFFUSION-TEACHER BRANCH

  • Diffusion segments follow deterministic (η = 0) DDIM sub-trajectories; the student predicts clean motion once per segment and matches teacher per-step x0 estimates at detached trajectory states.The diffusion objective uses endpoint matching on the DDIM trajectory.Source: §A.3 · p. 16

A.2 TRAINING ALGORITHM AND CONVENTIONS

  • Algorithm 1 gives the flow training iteration: TACD uses a capped supervision grid with velocity loss, while endpoint matching uses the original grid and endpoint loss.Only the online student receives gradients.Source: §A.3 · p. 16

A.3 DIFFUSION-TEACHER BRANCH

  • The flow branch uses π-Flow's single-knot DX policy on a fixed supervision grid, and a numerical check found loss, gradient, and window-average agreement to 10^−9 relative tolerance.Source: §A.3 · p. 17

C EXPERIMENTAL SETTINGS

  • The shared experimental settings appendix collects benchmark-specific models and training, evaluation protocol and model selection, and named training configurations.Source: C EXPERIMENTAL SETTINGS · p. 17

C.1 MODELS AND TRAINING

The experiments use HY-Motion, MDM, and Kimodo teachers with benchmark-specific student configurations and training recipes. The appendix also specifies evaluation protocols and the flow-control and diffusion endpoint-matching configurations.

C.1 MODELS AND TRAINING

  • The controlled HumanML3D comparison uses a frozen HY-Motion 1B teacher and Qwen3-8B encoder, with a 0.46B Lite student backbone and frozen Qwen3-0.6B encoder.The uncapped, TACD, and bound-enforcement comparisons share initialization, prompt cache, training budget, and eight-step inference.Source: §C.1 · p. 17
  • On KIT-ML, teacher-initialized rank-32 LoRA students at two, four, and eight steps use DDIM endpoint matching; training uses teacher supervision and no real motions.Source: §C.1 · p. 17
  • Kimodo students retain the teacher's 0.28B motion backbone, use low-rank adaptation and a Llama-3.2-1B encoder, and are evaluated at K ∈ {8, 4, 2}.The evaluation uses 607 prompts; latency is measured end-to-end for eight-second motions on one RTX L40.Source: §C.1 · p. 18

C.2 EVALUATION

  • HumanML3D and KIT-ML quality, alignment, and diversity metrics use dataset-specific text and motion evaluators and are averaged over 20 evaluator repetitions.Kimodo's TMR FID uses generated-motion and caption embeddings without real motions, so it is not comparable with HumanML3D FID.Source: §C.2 · p. 18
  • Reported trained rows are final fixed-budget iterates, not checkpoints selected by validation FID; primary HumanML3D student rows average three training seeds.KIT-ML TACD point estimates also average three seeds; its metric intervals reflect evaluator repetitions.Source: §C.2 · p. 18

C.3 TRAINING CONFIGURATIONS

  • Flow-control experiments use uniform grids at 1B/K = 4 and Lite/K = 8 with three seeds, while the bound uses δ = 1/(2K), C = 4K^2; diffusion experiments use endpoint matching.Table 7 identifies the flow grid-capping and diffusion endpoint-matching recipes as TACD configurations.Source: §C.3 · p. 19, Table 7 · p. 19

D BASELINE IMPLEMENTATIONS

The ports preserve method-specific objectives while sharing a common student, prompt cache, training budget, seeds, and evaluation protocol. Their training targets differ across distribution matching, consistency distillation, and rectified-flow distillation.

D BASELINE IMPLEMENTATIONS

  • All ports share the student architecture, prompt cache, seeds, generator-update budget, and evaluation protocol while retaining method-specific targets and hyperparameters.The student uses a 0.46B Lite motion head and Qwen3-0.6B conditioning path, with K=8 sampling and 8,000 generator updates.Source: D BASELINE IMPLEMENTATIONS · p. 19
  • The DMD port trains backward-simulated clean motion against frozen-teacher and learned-fake scores, with a teacher-pair regression term; neither term uses real motions.The fake network is updated five times per generator update, and the regression term has weight 1.Source: D BASELINE IMPLEMENTATIONS · p. 19
  • The consistency port first synthesizes teacher motions because HY-Motion’s training motions are unavailable, then applies consistency distillation to that synthetic corpus.It folds CFG into the student during training, which samples at CFG 1.Source: D BASELINE IMPLEMENTATIONS · p. 19
  • The reflow port interpolates noise and teacher outputs, then trains the student’s CFG-combined velocity to predict their difference at a stratified time in each segment.It uses teacher-generated couplings and no real motions; other settings are inherited from the TACD rows.Source: D BASELINE IMPLEMENTATIONS · p. 19

E RESULTS BY BENCHMARK

The appendix reports benchmark-specific quality comparisons for flow and diffusion teachers, alternate HumanML3D evaluation, KIT-ML, and Kimodo. Across these settings, TACD students are compared with teacher outputs or truncated samplers, alongside deployment measurements for Kimodo.

E RESULTS BY BENCHMARK

  • This appendix collects the complete quality-comparison tables for HumanML3D with flow and diffusion teachers, a second evaluator, KIT-ML, and Kimodo.The benchmark-specific results follow the main-text comparisons in Sections 4.2 and 4.4.Source: E RESULTS BY BENCHMARK · p. 20

E.1 HUMANML3D WITH THE FLOW TEACHER

  • TACD’s three-seed R@3 is 0.7821 versus the teacher’s 0.7431, while its FID is 1.0407 versus 0.5407; the teacher’s best FID and R@3 use CFG 5.0.Table 8 preserves the full teacher-guidance sweep; Table 1 includes published HumanML3D context.Source: §E.1 · p. 20, Table 8 · p. 20

E.2 DIFFUSION TEACHERS ON HUMANML3D

  • At matched NFE (K=4), TACD’s FID is 0.055 versus 0.072 for the V2 student, with higher MultiModality.Table 9 gives the full comparisons with the MLD and MotionLCM-V2 teachers.Source: §E.2 · p. 20, Table 9 · p. 20

E.3 A SECOND HUMANML3D EVALUATOR

  • Under the released 67-dimensional evaluator, TACD with HY-Motion remains the best eight-step system on every metric in each of its three seeds.The rescore uses 20 repetitions while retaining captions and lengths from the Guo evaluation protocol.Source: §E.3 · p. 21

E.4 KIT-ML

  • On KIT-ML, endpoint-matching TACD reduces MDM-teacher FID by 32% at two steps and 13% at four and eight steps, and beats the truncated teacher on all four metrics at every NFE.The four metrics are R@1, R@3, MM-Dist, and FID.Source: §E.4 · p. 21, Table 10 · p. 21, Table 11 · p. 21

F KIMODO

  • Kimodo evaluation uses a 607-prompt caption set and its released TMR evaluator; TACD uses none of the teacher’s training motions.GT-R@1 is restricted to the 567 prompts with ground-truth motions.Source: F KIMODO · p. 21

F.1 STEP COMPRESSION AND CONDITIONING

  • On Kimodo, eight-step TACD reaches R@1 71.39±0.50, R@3 86.55±0.25, and FID 0.0542 against teacher values 73.15, 88.63, and 0.045; its end-to-end speedup is 11.9×.The 1B-encoder student cuts VRAM from 15.3 to 4.0 GB; step compression accounts for 10.1× of the speedup and the encoder change for 1.18×.Source: §F.1 · p. 22, Table 12 · p. 22

F.2 TRAINING ON THE 1B ENCODER

These appendix sections examine Kimodo encoder choice and held-out prompts, document semantic-fidelity and human-ranking protocols, and list the controlled interventions and gradient analyses behind Section 4.3.

F.2 TRAINING ON THE 1B ENCODER

  • Training the student end-to-end on the 1B encoder leaves FID effectively unchanged (+0.0002, with per-seed standard deviations at most 0.0003) and R@3 flat versus the 8B encoder.The comparison uses three seeds per condition at K=8; the 8B-encoder rows are separate training runs from Table 12.Source: §F.2 · p. 22, Table 14 · p. 23

F.3 HELD-OUT SPLIT ANALYSIS

  • On held-out BONES-SEED prompts, TACD@8 has GT-R@1 88.6 versus 84.8 for the truncated teacher@8, a +3.8-point advantage.The held-out set contains 105 prompts; these clips are used only for evaluation, not student training.Source: §F.3 · p. 22

G SEMANTIC FIDELITY UNDER A VLM JUDGE

  • The VLM study scores semantic fidelity on 640 fixed prompts using video-question yes-rates, with paired prompt-cluster bootstrap comparisons across eight HY-Motion systems.The judge sees 14 frames from each six-second clip; the shared comparison set covers 2,571 gated questions across 636 prompts.Source: G SEMANTIC FIDELITY UNDER A VLM JUDGE · pp. 22–23

H HUMAN RANKING STUDY

  • The human study compares four systems on 50 stratified prompts, ranking prompt-following first and using naturalness only to break ties.Seventeen annotators contributed 691 rankings, with intervals from bootstrap resampling of annotators and prompts together.Source: H HUMAN RANKING STUDY · p. 23

I CONTROLLED INTERVENTIONS AND GRADIENT STATISTICS

  • The controlled-interventions appendix reports per-seed records and gradient statistics for supervision-grid controls, coefficient interventions, gradient probes, clipping, and the terminal-coefficient sweep.It also includes the full coefficient sweep in Appendix I.4.Source: I CONTROLLED INTERVENTIONS AND… · p. 23

I.1 SUPERVISION-GRID CONTROL ON THE 1B STUDENT

The appendix tests whether grid capping improves a four-step 1B student, then details coefficient interventions, gradient probes, and the terminal-coefficient sweep. It also identifies where the deployment-cost measurements are documented.

I.1 SUPERVISION-GRID CONTROL ON THE 1B STUDENT

  • Capping the supervision grid lowers mean FID from 3.291 to 1.458 on the 1B student at K=4.Clamping only the final supervision time yields FID 1.462 and matches the capped arm seed for seed in this configuration.Source: §I.1 · p. 24, Table 15 · p. 24

I.2 COEFFICIENT INTERVENTIONS BY SEED

  • Restoring the terminal coefficient on the capped grid raises mean FID to 2.669, versus 1.011 for weight capping.The restored-coefficient seed values are 2.6593, 2.6454, and 2.7029.Source: §I.2 · p. 24, Table 16 · p. 24

I.3 GRADIENT PROBES AND CLIPPING

  • At initialization and K=8, the terminal segment carries 68.3% of gradient on the original grid versus 0.86% and 0.89% on the capped grid for probe seeds 42 and 43.All arms share unit-norm clipping, which is active in essentially every logged observation; configurations differ in how gradient is composed across segments.Source: §I.3 · p. 24, Table 17 · p. 25

I.4 TERMINAL-COEFFICIENT SWEEP

  • For terminal coefficients up to 4096, FID stays between 1.0 and 1.07; it degrades progressively at larger coefficients, while above 4096 all five metrics move together at every step.The sweep changes one flag per arm and applies the same unit-norm clipping rule across configurations.Source: §I.4 · pp. 24–25, Table 18 · p. 25

J DEPLOYMENT COST

J.1 LATENCY AND MEMORY

Eight-step TACD reduces HY-Motion latency and memory relative to its teacher, with costs measured under a specified batch-1 RTX L40 protocol. The appendix also presents controlled teacher comparisons and a gallery of eight-step samples.

J.1 LATENCY AND MEMORY

  • Latency and memory measurements use batch 1 on one RTX L40, with median latency across 150 timed samples and peak allocator memory measured after loading.HY-Motion samples are 196 frames at CFG 5; Kimodo samples are eight seconds, and text encoding is timed separately from sampling.Source: §J.1 · p. 25, Table 19 · p. 25
  • 7.7× faster end to end than the teacher, TACD (HY-Motion) uses 2.62 GB versus 17.63 GB, a 6.7× memory reduction.It is also 5.5× faster than 50-step Lite; the student uses a 0.6B text encoder and 0.46B backbone, adding only a conditioning projection to Lite.Source: §J.1 · p. 25, Table 19 · p. 25
  • Training adds a rollout, K gradient-carrying student evaluations, and KM frozen-teacher queries per iteration, while inference NFE and deployment components remain unaffected by the EMA copy.These are training-only costs; the EMA copy does not affect deployment.Source: §J.1 · p. 25

K QUALITATIVE RESULTS

  • The qualitative appendix presents the teacher, its eight-step truncation, and TACD side by side, plus a gallery of compact-student samples.Source: K QUALITATIVE RESULTS · p. 28

K.1 TEACHER, TRUNCATED TEACHER, AND TACD

  • Figure 1 compares four prompts rendered by the 50-step teacher, its eight-step truncation, and eight-step TACD, sharing prompt, noise, frames, and camera within each row.The camera is fitted to the union of the three motions in each row.Source: §K.1 · p. 28

K.2 EIGHT-STEP GALLERY

  • Figures 7 and 8 show one eight-step TACD (HY-Motion) sample per prompt, with poses at evenly spaced times in each clip.A fixed yaw rotation is used for visualization and does not alter the motion.Source: §K.2 · p. 28

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