Secondary Dynamics Injection in 3D Animation

• Secondary Dynamics Injection (SDI) is a method that blends latent motion priors to animate realistic secondary dynamics, such as hair, skirts, and loose clothing.
• It uses a three-phase denoising process—blending, reference switching, and re-denoising—to merge skeletal geometry with intricate motion details.
• The strategy employs spatial masks and denoising thresholds to effectively inject pre-trained human motion priors, thereby enhancing the graphical fidelity of non-rigid animations.

Secondary Dynamics Injection (SDI) is a method introduced in “From Rigging to Waving: 3D-Guided Diffusion for Natural Animation of Hand-Drawn Characters” as part of a hybrid pipeline for hand-drawn character animation (Zhou et al., 8 Sep 2025). In that usage, SDI is an inference-time denoising strategy that injects motion priors from a pre-trained human video diffusion model into a domain-adapted stylized model, with the transfer restricted by spatial masks and by a selected denoising-timestep window. Its stated role is to enrich non-rigid secondary motion—especially hair, skirts, sleeves, and loose clothing—while retaining the geometric consistency obtained from rigging, motion retargeting, and coarse 3D-guided rendering (Zhou et al., 8 Sep 2025).

1. Concept and motivation

SDI is motivated by a division between “primary motion” and “secondary motion” in hand-drawn character animation. The underlying system combines skeletal animation and video diffusion rather than relying on either one alone. Skeletal retargeting and skinning provide geometry preservation and pose consistency, but “skinning-based deformation effectively generates primary motion” and “often fails to capture realistic secondary motion, such as cloth swaying or hair flowing.” At the same time, the stylized hand-drawn training set used for domain adaptation is described as small and focused on primary motions, so the domain-adapted diffusion model improves appearance and contours but still “more or less lacks the richness of secondary motion” (Zhou et al., 8 Sep 2025).

Within the full pipeline, a reference drawing $I_{\text{ref}}$ is converted into a contour-free reference $I^\text{nc}_{\text{ref}}$, a rough 3D character is reconstructed, and Hair Layering Modeling may be applied to separate hair from the body before rigging. After retargeting a target 3D motion $\mathcal{P}$ onto the final geometry $\mathcal{G}$, the system renders a pose sequence $\{P_{1:N}\}$, a coarse color sequence $\{C_{1:N}\}$, and an SDI mask sequence $\{M_{1:N}^{\text{SDI}}\}$. The coarse frames are then masked as

$$\{C^{\text{masked}}_{1:N}\}=\{C_{1:N}\}\cdot(1-M_{1:N}^{\text{SDI}}),$$

so the masked regions can later be regenerated rather than preserved from the coarse animation (Zhou et al., 8 Sep 2025).

This positioning is essential. SDI is not a stand-alone animation method; it is a motion-prior transfer mechanism embedded in the refinement stage of a hybrid 3D-guided diffusion system. The geometry-preserving proxy supplies pose and coarse structure, while SDI is reserved for regions where stylized animation requires delayed, non-rigid, inertia-like behavior.

2. Latent-space formulation

The diffusion model operates in latent space using a VAE encoder $E(\cdot)$ and decoder $D(\cdot)$. For an image $I^\text{nc}_{\text{ref}}$0 and latent $I^\text{nc}_{\text{ref}}$1, the forward process is

$I^\text{nc}_{\text{ref}}$2

Here $I^\text{nc}_{\text{ref}}$3 is the noisy latent at diffusion step $I^\text{nc}_{\text{ref}}$4, $I^\text{nc}_{\text{ref}}$5 is Gaussian noise, and $I^\text{nc}_{\text{ref}}$6 are the noise-schedule coefficients. The method uses v-prediction with

$I^\text{nc}_{\text{ref}}$7

and trains the denoiser with

$I^\text{nc}_{\text{ref}}$8

During sampling, the noise-free latent estimate is

$I^\text{nc}_{\text{ref}}$9

The paper identifies $\mathcal{P}$0 as indicating the denoising direction in the v-prediction process, and SDI acts precisely at that level (Zhou et al., 8 Sep 2025).

The domain-adapted model is denoted $\mathcal{P}$1 and is based on UniAnimate with minor modifications. A coarse prior encoder $\mathcal{P}$2 embeds the masked coarse color sequence together with the SDI masks; these inputs are concatenated along the channel dimension and processed by a lightweight spatiotemporal encoder consisting of “two 2D convolutional layers and a temporal Transformer layer.” The resulting embeddings are concatenated with the input noise and fed into the denoising UNet. SDI then augments this stylized denoising process by consulting the original pre-trained UniAnimate model $\mathcal{P}$3, which is described as richer in human motion priors because it was trained on real human videos (Zhou et al., 8 Sep 2025).

The central SDI equation blends the clean latent estimates of the two models for frame $\mathcal{P}$4 at timestep $\mathcal{P}$5: $\mathcal{P}$6 Here $\mathcal{P}$7 is the SDI mask downsampled to latent resolution. Values near 1 select the pre-trained model’s estimate, and values near 0 keep the domain-adapted estimate. The injected quantity is therefore the pre-trained model’s clean latent estimate, or equivalently the denoising direction implied by $\mathcal{P}$8. The paper explicitly distinguishes this from attention-map injection, residual feature fusion inside specific UNet blocks, ControlNet-like branches, or any separate learned adapter (Zhou et al., 8 Sep 2025).

3. Three-phase denoising procedure

The SDI generation process is divided into three phases with thresholds $\mathcal{P}$9 and $\mathcal{G}$0, where

$\mathcal{G}$1

The first phase, over timesteps $\mathcal{G}$2, uses only the domain-adapted model $\mathcal{G}$3, conditioned on the contour-free reference image $\mathcal{G}$4. This stage is intended to establish structure, identity, and primary motion aligned with the stylized character. The use of $\mathcal{G}$5 begins what the paper calls reference switching, motivated by the observation that the pre-trained human model handles contour lines poorly and may misinterpret stylized reference semantics (Zhou et al., 8 Sep 2025).

The second phase, over $\mathcal{G}$6, computes latent estimates from both $\mathcal{G}$7 and $\mathcal{G}$8 and applies the masked blend. Injection is therefore confined to an intermediate-early portion of denoising rather than the full trajectory. This choice follows an empirical observation reported by the authors: early denoising steps determine spatial structure, later steps refine texture, and within the structure-forming portion, primary motion emerges first while secondary motion appears gradually afterward. SDI accordingly intervenes when motion distribution is still being established but before texture refinement dominates (Zhou et al., 8 Sep 2025).

The third phase begins after the blend stage ends at $\mathcal{G}$9. Rather than continuing the same chain with the contour reference restored, the system decodes the blended latent estimate

$\{P_{1:N}\}$0

uses the decoded intermediate video to inpaint the missing masked regions of the coarse guidance sequence, and applies Poisson Blending to produce $\{P_{1:N}\}$1. It then restarts from the original initial noise $\{P_{1:N}\}$2 and re-denoises from scratch using only $\{P_{1:N}\}$3, now conditioned on the original contour reference $\{P_{1:N}\}$4 and the updated coarse guidance enriched with the inserted dynamics. This re-denoising stage is described as necessary to restore contour fidelity and stylized appearance while preserving the motion patterns inserted during the blend phase (Zhou et al., 8 Sep 2025).

In this formulation, SDI is inseparable from reference switching and re-denoising. Blending alone transfers motion priors, but the full procedure converts that transferred motion into an updated coarse prior and then asks the stylized model to redraw the result coherently in the target contour language.

4. Training status, masks, and system boundaries

SDI is explicitly not a separately trained module. The domain-adapted model $\{P_{1:N}\}$5 is trained beforehand on the stylized dataset, but “there is no SDI-specific training loss.” The only loss shown is the general v-prediction diffusion loss. Training is intentionally conservative: the spatial layers are fine-tuned to adapt stylized appearance, while the temporal layers are frozen “to maintain the real-world motion prior.” The coarse prior encoder $\{P_{1:N}\}$6 is trained jointly with the tuned spatial layers under the same diffusion objective. The pre-trained model $\{P_{1:N}\}$7 serves as the source of motion priors and is not described as being further optimized for SDI (Zhou et al., 8 Sep 2025).

The masks used by SDI are user-provided on front and back views, back-projected onto the mesh, and rendered across all frames. The paper states that “a value of 1 indicates the regions to be enhanced and a value of 0 indicates the regions to be preserved.” Typical target regions are hair ends and skirts. Directly in the blend equation, these masks localize where motion priors from $\{P_{1:N}\}$8 are injected; outside the mask, the latent estimate remains that of the domain-adapted stylized model (Zhou et al., 8 Sep 2025).

The paper also delineates SDI from Hair Layering Modeling (HLM). HLM addresses a geometry problem caused by low-poly single-mesh reconstruction, especially when long hair sticks unnaturally to shoulders or torso during rigging. SDI addresses a distinct motion problem: even with improved geometry and rigging, skeletal motion still lacks realistic non-rigid secondary dynamics. HLM therefore improves the proxy geometry and deformation baseline, whereas SDI improves motion realism during diffusion refinement.

5. Empirical behavior and ablation evidence

The principal empirical claim is qualitative but explicit: “compared with only using the domain-adapted model without SDI, our SDI strategy effectively generates secondary dynamics, extending beyond the primary dynamics.” The detailed ablations separate three components—blending, reference switching, and re-denoising—and show that the complete procedure is required to obtain both richer motion and stylized visual consistency (Zhou et al., 8 Sep 2025).

Variant	Procedure	Reported behavior
W/o SDI	Only $\{P_{1:N}\}$9 with $\{C_{1:N}\}$0	Captures primary motion but not secondary dynamics
Bld	Blend $\{C_{1:N}\}$1 and $\{C_{1:N}\}$2 with $\{C_{1:N}\}$3	Introduces motion, but contour patterns can be misplaced into internal regions
Bld+RS	Blend with $\{C_{1:N}\}$4, then switch to $\{C_{1:N}\}$5	Improves contour handling, but discrepancies and contour-style inconsistency remain
Bld+RS+RD	Blend, rebuild coarse guidance, then re-denoise from scratch	Restores stylized consistency while retaining injected dynamics

The parameter studies support the same interpretation. Increasing $\{C_{1:N}\}$6, which determines when injection begins, strengthens motion intensity, but if $\{C_{1:N}\}$7 is too small, the output resembles the no-SDI case, whereas very high values such as 0.95 can introduce artifacts. Varying $\{C_{1:N}\}$8, which determines when the blend phase ends, has little visible effect on final results, and the paper recommends $\{C_{1:N}\}$9 or $\{M_{1:N}^{\text{SDI}}\}$0 as a runtime-quality compromise. The implementation section recommends

$\{M_{1:N}^{\text{SDI}}\}$1

Inference uses a DDIM sampler with 20 steps. For a 32-frame $\{M_{1:N}^{\text{SDI}}\}$2 video, reported runtimes are 45 seconds without SDI and 72, 81, and 90 seconds with SDI for $\{M_{1:N}^{\text{SDI}}\}$3, respectively. The paper also notes that “only early denoising steps influence the motion distribution,” so reducing $\{M_{1:N}^{\text{SDI}}\}$4 below 0.7 yields minimal motion benefit while increasing processing time (Zhou et al., 8 Sep 2025).

These ablations define SDI’s practical meaning. It is not merely latent blending; it is a composite inference strategy in which blending provides motion priors, reference switching prevents contour confusion, and re-denoising restores stylized consistency.

6. Terminological boundaries and neighboring uses

Within the supplied literature, SDI is explicitly named only in the hand-drawn character animation pipeline just described (Zhou et al., 8 Sep 2025). The phrase does not appear in the dependency-injection anti-pattern catalog (Laigner et al., 2021), in the plasma-accelerator study of refluxing electron injection at a sharp vacuum–plasma transition (Hu et al., 2017), in the theory of spin-current-driven dynamics in textured noncollinear antiferromagnets (Yamane et al., 2019), in the analysis of contractile injection systems (Toyonaga et al., 2024), in nonlinear self-injection locking of microresonator solitons (Voloshin et al., 2019), or in tunneling-injection quantum-dot semiconductor optical amplifiers (Khanonkin et al., 2018). Those works address different meanings of “injection,” and the supplied details explicitly state that they do not use the term SDI (Laigner et al., 2021, Hu et al., 2017, Yamane et al., 2019, Toyonaga et al., 2024, Voloshin et al., 2019, Khanonkin et al., 2018).

Two nearby usages are distinct rather than equivalent. In microgrids, “secondary false data injection attack” refers to additive malicious bias signals injected into communication links that drive distributed secondary control dynamics (Liu et al., 2024). In turbulent neutron-star-core modeling, an “anomalous secondary injection mechanism” denotes a reverse transfer of energy from the quantum-pressure sector into incompressible kinetic energy after spin-down (Sivakumar et al., 25 Jun 2025). These are secondary-injection concepts in their own domains, but neither defines Secondary Dynamics Injection as a diffusion-based animation method.

The restricted scope of the term is therefore important. In current arXiv usage represented by the supplied data, SDI denotes a specific latent-space motion-prior injection strategy for stylized animation, not a generic label for any secondary, dynamic, or injection-related process.