Predictive Caching Scheduler Constraint

• PCSC is a dynamic caching scheduler that optimizes inference by balancing computational cost with error control in diffusion-based generative models.
• It employs a three-phase scheme in Fast3Dcache and dynamic programming in Diffusion Policy to schedule updates based on voxel stabilization and cosine similarity metrics.
• Empirical studies show PCSC improves throughput up to 27% and reduces FLOPs by over 50% while maintaining near-lossless geometric and policy fidelity.

The Predictive Caching Scheduler Constraint (PCSC) is a central module in modern training-free acceleration frameworks for iterative neural generative models—most notably, in 3D diffusion-based geometry synthesis (Fast3Dcache) and in transformer-based Diffusion Policy. PCSC dynamically determines a cache schedule for latent feature tokens or block outputs across denoising timesteps, balancing computational savings with fidelity by anticipating or constraining error accumulation. PCSC frameworks analyze stabilization patterns, data-driven feature similarities, and hierarchical error propagation to implement aggressive yet safe caching; they underpin state-of-the-art results in throughput and compute reduction while ensuring geometric and policy consistency (Yang et al., 27 Nov 2025, Ji et al., 16 Jun 2025).

1. Formal Definition and Theoretical Foundations

PCSC operationalizes the problem of scheduling updates for intermediate representations, such as feature tokens or transformer block outputs, under computational budget and stability constraints. In Fast3Dcache, PCSC determines, at each diffusion timestep $t$, how many latent-feature tokens may be cached and how many must be freshly recomputed, based on observed stabilization of voxel occupancy. The scheduler enforces a dynamic quota adapting to the current denoising phase: minimal caching during early formation, increasing cache rates as stabilization emerges, and aggressive/fixed-ratio caching when only minor geometric refinements occur.

In block-wise adaptive caching for Diffusion Policy, PCSC determines a globally optimal set of update steps $\mathcal{C}$ for each block over $K$ denoising steps, constrained by a budget $|\mathcal{C}|=M$. The objective is to maximize the cumulative similarity between actual and cached features,

$$\max_{\mathcal{C}\subseteq\{1,\dots,K\},\;|\mathcal{C}|=M} \;\sum_{m=0}^{M} \phi\left(c_m,\,c_{m+1}-1\right)$$

with $c_0=0$, $c_{M+1}=K$, and $\phi(i,j)=\sum_{t=i+1}^j s_t$ the cumulative cosine similarity between consecutive block features, ensuring updates synchronize with periods of low feature drift (Ji et al., 16 Jun 2025). This dynamic programming-based approach identifies safe skip intervals predictable from offline analysis.

2. Scheduling Methodologies and Mathematical Formulation

In 3D geometry synthesis via Fast3Dcache, the PCSC scheduler leverages a three-phase pattern of voxel stabilization:

• Phase 1 (formation): $c_t=0$, no caching. Geometry formation is highly dynamic.
• Phase 2 (stabilization): Cache quota increases log-linearly as the number of “dynamic” voxels decays. The number of flipped voxels $\Delta s_t$ is measured as

$$\Delta s_t = \sum_{i,j,k} \bigl(\mathcal{O}_{t+1}(i,j,k)\oplus\mathcal{O}_t(i,j,k)\bigr).$$

At anchor timestep $t_a = \lceil N\cdot\rho_a\rceil$, the measured value $\sigma=\Delta s_{t_a}$ seeds an exponential decay

$$\Delta\hat{s}_t = \sigma\,\exp\bigl(\mu\,(t-t_a)\bigr)$$

translated to a cache quota

$$c_t = D^3 - \frac{\Delta\hat{s}_t}{\gamma_{\rm up}}.$$

• Phase 3 (refinement): Fixed-ratio caching, $c_t = \xi\,D^3$, interleaved with full-correction steps.

In block-wise Diffusion Policy, the Adaptive Caching Scheduler operates per-block using the (offline) statistics of feature drift (cosine similarities), producing per-block update step sets via dynamic programming. Additional constraints, dubbed Bubbling Union, guarantee upstream blocks update whenever downstream FFN blocks update, preventing error surges due to inter-block staleness (Ji et al., 16 Jun 2025).

3. Pseudocode and Operational Workflow

PCSC is integrated as part of a diffusion model’s inference loop. In Fast3Dcache, the control flow is:

• Phase detection: Based on current step $k$ and pre-set ratios ($\rho_a$, $\rho_{\rm CFG\_OFF}$).
• Cache-quota computation: $c_t=0$ (Phase 1), $c_t$ by log-linear schedule (Phase 2), or $c_t=\xi D^3$ (Phase 3). Full correction enforced every $f_{\rm corr}$ steps in Phase 3.
• Stable token selection: The Spatiotemporal Stability Criterion (SSC) ranks tokens by a convex combination of normalized acceleration and velocity:

$$C_i(t) = \omega\,\mathrm{norm}(A_i(t)) + (1-\omega)\,\mathrm{norm}(V_i(t)),$$

with $V_i(t)=\lVert v_i(t)\rVert_2$ and $A_i(t)=\lVert v_i(t)-v_i(t-1)\rVert_2$.

• Transformer application: Only active (non-cached) tokens are recomputed; cached tokens are reused.

In block-wise adaptive caching, the workflow comprises offline (per-task) calibration of the feature-similarity matrix, dynamic programming to produce the per-block update schedule, and union propagation of update steps upstream. Inference then simply checks $k\in\mathcal{C}_b$ for each block to decide between update and reuse, with no runtime scheduler cost.

4. Interactions with Stability Criteria, Error Control, and Constraints

PCSC itself determines how many features to cache, while selection of which features is delegated to modules such as SSC. SSC selects the lowest-scoring (most stable) tokens for caching, using per-token spatiotemporal dynamics. Additionally, PCSC frameworks implement error-control rules:

• Full-sampling steps: To limit accumulated drift, complete recomputation is periodically enforced after $\tau$ cached steps.
• Bubbling Union (Diffusion Policy): Any update in a downstream FFN block forces simultaneous updates in identified upstream blocks with high error potential, truncating inter-block error propagation. This guarantees lossless, numerically stable caching per block (Ji et al., 16 Jun 2025).

Such mechanisms ensure that error does not accumulate unboundedly, preserving geometric or action fidelity throughout the iterative denoising process.

5. Hyperparameters, Tuning, and Their Impact

PCSC involves several key hyperparameters, each balancing geometric/policy fidelity against computational gain:

Hyperparameter	Role / Effect	Typical Value(s)
$\rho_a$ (anchor ratio)	End of Phase 1; higher = safer, less acceleration	0.2–0.3
$\mu$ (decay slope)	Cache quota increase rate (Phase 2)	$-0.07$ (optimal)
$\gamma_{\rm up}$	Voxel-token upsampling factor	(fixed; architecture)
$\tau$	Interval for full refresh, bounding drift	8
$\xi$	Fixed cache quota in Phase 3	0.7
$\omega$ (SSC weight)	Velocity vs. acceleration in $C_i(t)$	0.7
$f_{\rm corr}$	Full-correction cadence in Phase 3	every 3 steps

Ablation in Fast3Dcache establishes that $\mu=-0.07$ gives optimal quality/speed tradeoff, while orders-of-magnitude perturbations degrade fidelity. Joint use of velocity and acceleration metrics in SSC outperforms either alone (Yang et al., 27 Nov 2025). In block-wise adaptive caching, the compute budget $M$ and per-block selection of unioned update steps are crucial for lossless acceleration (Ji et al., 16 Jun 2025).

6. Empirical Performance and Impact

PCSC modules consistently outperform fixed-rate or purely heuristic caching under modern diffusion architectures. In Fast3Dcache, ablation shows that:

• Without PCSC: Fixed 25%/12.5% sampling yields significantly higher geometric error (CD 0.0956/0.0899) and lower F-Score (34.51%/39.06%).
• With PCSC ($\mu=-0.07$): Achieves CD 0.0697 (1.6% above non-accelerated baseline) and F-Score 54.09% (–1.34% loss), while reducing FLOPs by 41% and boosting throughput by 25%. On TRELLIS with $\tau=8$, throughput improves by 27.12%, FLOPs drop by 54.8%, with only +2.48% CD and –1.95% F-Score relative to vanilla inference (Yang et al., 27 Nov 2025).

In block-wise adaptive caching for Diffusion Policy, the dynamic programming-based scheduler alongside Bubbling Union ensures numerical identity of generated actions to the full-compute baseline, with up to 3x acceleration in inference observed empirically (Ji et al., 16 Jun 2025).

7. Broader Implications and Extensions

PCSC is a dynamic, data-driven constraint mechanism that enables aggressive, training-free caching schedules without sacrificing fidelity in iterative generative models. By aligning computation skipping with empirically observed or data-predicted feature stability and enforcing principled error propagation constraints, it allows deployment of diffusion and policy models in computationally constrained or real-time settings previously inaccessible to naïve acceleration strategies.

The core methodologies of PCSC—stabilization pattern exploitation, global similarity maximization under budget, inter-module error propagation control—are broadly applicable beyond 3D geometry synthesis and actuator policy acceleration, potentially impacting a wide range of denoising-based generation tasks. The use of offline-derived, instance-independent schedules further supports robust applicability in homogeneous but compute-sensitive domains. The lossless or near-lossless regime established by current schedulers, combined with their zero-scheduler-overhead inference pathways, represents a state-of-the-art solution for caching-based model acceleration (Yang et al., 27 Nov 2025, Ji et al., 16 Jun 2025).