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From Local Mismatch to Global Impact: Optimizing Cache Reuse Policy for Efficient Diffusion

Xichen Ye, Yifan Wu, Zhikang Xie, Xiangyu Yue, Cheng Jin, Weizhong Zhang

Year: 2026Venue: arXiv preprintArea: cs.AIType: PreprintEmbeddings: 108

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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%

Last extracted: 8/14/2026, 5:49:14 AM

Summary

The paper introduces Global-Impact Cache (GCache), a method for optimizing cache reuse policies in diffusion models. It identifies that existing local similarity heuristics misalign with global generation quality due to non-uniform error propagation. GCache establishes a theoretical error propagation upper bound and reformulates policy search as a bilevel optimization problem, reparameterizing the propagation exponent with a Bernstein form to align theoretical estimates with empirical loss. Experiments show GCache outperforms prior strategies, achieving a 2.17x speedup with improved quality on the Wan2.1 model.

Entities (7)

GCache · method · 98%Wan2.1 · model · 95%LPIPS · metric · 92%Bilevel Optimization · optimization-technique · 90%ERTACache · method · 90%Bernstein form · mathematical-concept · 88%Flux-dev 1.0 · model · 85%

Relation Signals (5)

GCache → appliedto → Wan2.1

confidence 96% · on the state-of-the-art Wan2.1 video diffusion model, GCache maintains a 2.17x speedup

GCache → outperforms → ERTACache

confidence 95% · GCache consistently outperforms prior caching strategies... compared to the state-of-the-art ERTACache

GCache → reduces → LPIPS

confidence 94% · reducing LPIPS from 0.1095 to 0.0316

GCache → formulates → Bilevel Optimization

confidence 93% · reformulate cache policy search as a bilevel optimization problem

GCache → uses → Bernstein form

confidence 92% · we further reparameterize the propagation exponent with a Bernstein form

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Abstract

Abstract:Diffusion models have achieved dominant performance in visual generation but suffer from substantial inference overhead. While cache-based acceleration has emerged as a promising solution, existing policies rely on local similarity heuristics, which we identify as being significantly misaligned with final generation quality. This discrepancy stems from the non-uniform propagation and accumulation of errors along the denoising trajectory. To address this, we propose Global-Impact Cache (GCache). We first establish a rigorous theoretical characterization of the error propagation upper bound. Recognizing that this bound can be overly conservative for complex, highly non-convex diffusion models, we further reparameterize the propagation exponent with a Bernstein form and reformulate cache policy search as a bilevel optimization problem. In detail, GCache identifies an optimal reuse policy in the inner objective while aligning the error-weighting function with generation quality loss in the outer objective. This framework effectively reconciles theoretical rigor with empirical performance, learning to prioritize computation where it most impacts visual fidelity. Extensive experiments demonstrate that GCache consistently outperforms prior caching strategies on both video and image generation. Notably, on the state-of-the-art Wan2.1 video diffusion model, GCache maintains a 2.17x speedup while significantly enhancing generation quality, reducing LPIPS from 0.1095 to 0.0316.

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From Local Mismatch to Global Impact: Optimizing Cache Reuse Policy for Efficient Diffusion Xichen Ye Yifan Wu Affiliation: Faculty of Engineering, The Chinese University of Hong Kong Zhikang Xie Xiangyu Yue Affiliation: Faculty of Engineering, The Chinese University of Hong Kong Cheng Jin Weizhong Zhang Thanks: Corresponding author Affiliation: School of Data Science, Fudan University [3pt] College of Computer Science Artificial Intelligence Fudan University Abstract Diffusion models have achieved dominant performance in visual generation but suffer from substantial inference overhead. While cache-based acceleration has emerged as a promising solution, existing policies rely on local similarity heuristics, which we identify as being significantly misaligned with final generation quality. This discrepancy stems from the non-uniform propagation and accumulation of errors along the denoising trajectory. To address this, we propose Global-Impact Cache (GCache). We first establish a rigorous theoretical characterization of the error propagation upper bound. Recognizing that this bound can be overly conservative for complex, highly non-convex diffusion models, we further reparameterize the propagation exponent with a Bernstein form and reformulate cache policy search as a bilevel optimization problem. In detail, GCache identifies an optimal reuse policy in the inner objective while aligning the error-weighting function with generation quality loss in the outer objective. This framework effectively reconciles theoretical rigor with empirical performance, learning to prioritize computation where it most impacts visual fidelity. Extensive experiments demonstrate that GCache consistently outperforms prior caching strategies on both video and image generation. Notably, on the state-of-the-art Wan2.1 video diffusion model, GCache maintains a 2.17×2.17× speedup while significantly enhancing generation quality, reducing LPIPS from 0.10950.1095 to 0.03160.0316. 1 Introduction In recent years, diffusion models [9, 27, 6, 13] have emerged as the dominant paradigm in visual generation, delivering high-fidelity and diverse outputs across various modalities, including images [22, 24] and videos [1, 3]. Despite these successes, diffusion models remain burdened by substantial inference overhead, stemming from the iterative nature of solving the underlying Ordinary Differential Equations (ODEs), which necessitates numerous model evaluations for a single sample. To mitigate this limitation, various acceleration mechanisms have been explored from multiple directions, including model-centric compression [8, 2], advanced sampling solvers [16, 33, 35], and, more recently, cache-based mechanisms [5, 14, 21]. Among current acceleration strategies, cache-based methods provide a practical approach to speeding up diffusion inference. Unlike model-centric techniques, caching avoids intensive retraining or distillation of model parameters and remains orthogonal to advanced sampling solvers, making it a highly lightweight solution for denoising acceleration. The primary objective is to establish an inference-time policy that identifies redundant intermediate residuals across adjacent timesteps to avoid repeated computations. While initial approaches [5, 25, 36] relied on uniform reuse schedules, they lacked the flexibility to adapt to varying residual dynamics across different timesteps. Consequently, recent works [14, 21] have shifted toward non-uniform strategies. These methods employ local similarity metrics to quantify the mismatch between target and cached residuals, triggering reuse only when the discrepancy is sufficiently small. Figure 1: Comparison between local mismatch and global impact (lower is better). We conduct a series of independent experiments in which a cached residual is reused at exactly one specific timestep. For each timestep, the blue marker (Rel-L1) measures the local discrepancy between the ground-truth residual and the cached residual from the preceding step, while the red marker (LPIPS) reflects the resulting impact on final generation quality. Despite these advancements, existing approaches remain limited by their reliance on local similarity metrics, such as the relative ℓ1 _1 distance. However, empirical evidence suggests that such locally-based strategies fail to accurately capture how individual cache reuse decisions affect final generation quality. As illustrated in Figure 1, large local discrepancies may correspond to only minor perceptual degradation: pronounced relative ℓ1 _1 spikes occur around step 1911 1 The prominent Rel-L1 spike around step 19 is a known characteristic of Flux-dev 1.0 under the Euler ODE solver. Similar spike behaviors across diffusion models have also been reported in prior work [14]. and increase sharply in the final denoising stages, yet result in only marginal increases in LPIPS. This mismatch reveals that local discrepancy alone is an unreliable proxy for global generation impact, indicating that effective cache reuse policies must account for both local reuse errors and their cumulative impact on final generation quality. To this end, we first establish a theoretical characterization of the error propagation dynamics in cache-reused diffusion trajectories. This analysis provides a principled foundation by relating local discrepancies to a global cumulative error bound, offering a rigorous heuristic for policy optimization. While this analytical bound serves as a robust guide, its worst-case nature inherently introduces a pessimistic bias, as it does not fully account for the high non-convexity and intrinsic error-resilience of diffusion models. To bridge this gap and unlock the full potential of our theoretical framework, we propose Global-Impact Cache (GCache). In detail, we parameterize the propagation exponent in the theoretical bound as a Bernstein form and formulate the policy search as a bilevel optimization problem, where the inner objective identifies the optimal reuse policy that minimizes the current error bound for a given set of parameters, while the outer objective optimizes the propagation parameters by minimizing empirical generation loss. In this way, GCache learns an error-weighting function that better reflects empirical error propagation, leading to more informed cache reuse decisions and improved generation quality. Extensive experiments across multiple image and video generation models demonstrate that our method, GCache, consistently outperforms prior caching strategies. Overall, we summarize our contributions as follows: • We identify a fundamental misalignment between local cache reuse errors and global generation quality, and provide a theoretical analysis that characterizes how cache reuse errors propagate during diffusion sampling, establishing an analytical upper bound on their global impact. • We demonstrate that there is an estimative gap between this theoretical bound and empirical error behavior, observing that the bound’s worst-case assumptions can be conservatively biased in the context of highly non-convex diffusion dynamics. • Motivated by this, we propose GCache, which reparameterizes the error propagation exponent with a Bernstein form and formulates cache reuse policy search as a bilevel optimization problem to better align theoretical estimates with empirical error behavior. • We conduct extensive experiments on both image and video generation tasks, demonstrating that GCache consistently achieves superior speed–quality trade-offs compared to existing cache-based acceleration methods. 2 Preliminaries In this section, we briefly review the background on diffusion models and cache reuse to establish notation and context. Further discussions of related work are provided in Appendix C. 2.1 Diffusion Models Diffusion models [9, 27, 13] synthesize samples by gradually perturbing real data ∼pdata() x p_data( x) into prior noise ∼pprior() n p_prior( n) (e.g., a standard Gaussian distribution ⁡(,)N( 0,I)), subsequently learning to invert this process for sample generation. Recent works [7] frequently adopt the Flow Matching paradigm [13]. Specifically, given a data-noise pair (,)( x, n), a flow path is constructed as t=(1−t)+t x_t=(1-t) x+t n for t∈[0,1]t∈[0,1], which induces the conditional velocity field: t(t∣)=dt[(1−t)+t]=−. v_t( x_t x)= ddt [(1-t) x+t n ]= n- x. (1) Since a specific t x_t can result from various (,)( x, n) pairs, Flow Matching targets the marginal velocity field: ⁡(t,t):=pt(∣t)[t(t∣)]. v( x_t,t):=E_p_t( x x_t) [ v_t( x_t x) ]. (2) A neural network θ v_θ is trained to approximate this marginal field by minimizing the conditional Flow Matching loss: ℒCFM(θ)=t,,‖θ(t,t)−t(t∣)‖22.L_CFM(θ)=E_t, x, n \| v_θ( x_t,t)- v_t( x_t x) \|_2^2. (3) This objective is equivalent to minimizing the Flow Matching loss ℒFM(θ)=t,pt(t)‖θ(t,t)−⁡(t,t)‖22L_FM(θ)=E_t,p_t( x_t)\| v_θ( x_t,t)- v( x_t,t)\|_2^2, effectively fitting the model to the true marginal velocity. During inference, samples are generated by solving the corresponding ordinary differential equation (ODE): dtt=⁡(t,t), ddt x_t= v( x_t,t), (4) initialized at 1∼pprior x_1 p_prior and integrated backward to t=0t=0. The final sample is given by 0=1−∫01⁡(τ,τ)τ x_0= x_1- _0^1 v( x_τ,τ)dτ. In practice, this integral is approximated using numerical ODE solvers. For instance, the Euler method discretizes the trajectory over N timesteps 1=tN>tN−1>⋯>t2>t1=01=t_N>t_N-1>·s>t_2>t_1=0, computing each step as: ti=ti+1−(ti−ti+1)(ti+1,ti+1). x_t_i= x_t_i+1-(t_i-t_i+1) v( x_t_i+1,t_i+1). (5) 2.2 Cache Reuse The primary inference bottleneck in diffusion models arises from the repetitive model evaluations necessitated by the ODE solver. Cache reuse has emerged as a promising strategy to mitigate this overhead by leveraging the temporal redundancy of intermediate representations across sampling steps. A prevalent approach involves reusing residual mappings across specific model layers [5]. Formally, consider a feed-forward neural network (e.g., a Transformer [29]) decomposed as: ⁡(t,t)=(fout∘fmid∘fin)(t,t), v( x_t,t)=(f_out f_mid f_in)( x_t,t), (6) where fmidf_mid represents the intermediate blocks (e.g., core transformer layers), while finf_in and foutf_out denote the layers responsible for input embedding and output projection (e.g., patchify and unpatchify), respectively. Let t:=fin(t) h_t:=f_in( x_t) and t:=fmid(t) z_t:=f_mid( h_t), the residual is then defined as t:=t−t. δ_t:= z_t- h_t. (7) During the sampling process, a cache reuse policy ∈0,1N m∈\0,1\^N governs the use of a stored residual c δ^c. At each timestep tnt_n, the policy determines whether to approximate the state by reusing the cached residual (ti=0 m_t_i=0): tic=c+ti, z^c_t_i= δ^c+ h_t_i, (8) or to perform a full computation and update the cache (ti=1 m_t_i=1): c←ti. δ^c← δ_t_i. (9) The objective of a cache reuse policy is to minimize the degradation of generation quality subject to a specific computational budget, which is typically defined by the total number of cache reuses, ‖0\| m\|_0. To develop effective caching policies, recent studies [14, 21] typically employ a local error metric, specifically the relative ℓ1 _1 distance, to determine whether to reuse the previously cached residual c δ^c at timestep tit_i: d⁡(c,ti)=‖c−ti‖1‖c‖1.d( δ^c, δ_t_i)= \| δ^c- δ_t_i\|_1\| δ^c\|_1. (10) However, as we demonstrate below, this local-only perspective fails to account for the error propagation inherent in the denoising process, ultimately resulting in sub-optimal caching decisions. 3 Method In this section, we begin with preliminary experiments that reveal the error propagation behavior in the denoising process (Section 3.1). We then develop a theoretical upper bound that characterizes how local cache reuse errors propagate across timesteps (Section 3.2). Since directly optimizing cache reuse policies with this bound proves insufficient in practice, we further refine it via a bilevel optimization framework and propose Global-Impact Cache (GCache) with an efficient solution strategy (Section 3.3). 3.1 Motivation Figure 2: Characterization of error propagation across the denoising trajectory. To motivate our study, we first conduct controlled perturbation experiments on video generation. Specifically, we inject random noise of a fixed magnitude into intermediate feature maps at different denoising timesteps and track the log-scaled deviation ‖t−^t‖1\| x_t- x_t\|_1 over subsequent denoising steps, where t x_t and ^t x_t denote the unperturbed and perturbed states. As illustrated in Figure 2, Perturbations introduced earlier are progressively amplified and lead to substantially larger final deviations than those injected later. These findings reveal a cumulative and time-dependent error propagation effect, suggesting that an effective cache reuse policy should account for not only the local cache reuse error but also the error propagation inherent in the denoising process. Building on this observation, the following subsection establishes a formal relationship between local reuse discrepancies and their cumulative propagation. 3.2 Error Propagation of Cache Reuse To rigorously quantify how local cache reuse errors accumulate across the denoising trajectory, we first establish a formal theoretical framework. Building on the empirical insights from Section 3.1, we aim to derive an upper bound for the final generation error that accounts for the time-dependent nature of error propagation. We first introduce the following regularity conditions, which are standard in the analysis of diffusion-based generative models [4]. Assumption 3.1 (Regularity and Approximation Conditions). For all denoising timesteps t∈[t1,tN]t∈[t_1,t_N], we assume the following conditions hold: (i) Bounded Approximation Error: The empirical velocity field θ v_θ approximates the ground-truth marginal velocity v with a uniform error bound η≥0η≥ 0, i.e., ‖⁡(,t)−θ(,t)‖1≤η \| v( x,t)- v_θ( x,t) \|_1≤η for all x and t. (i) Lipschitz Continuity: The output projection foutf_out is LoutL_out-Lipschitz continuous, and the learned velocity field θ v_θ is LtL_t-Lipschitz continuous with respect to its first argument, i.e., ‖θ(,t)−θ(,t)‖1≤Lt‖−‖1\| v_θ( x,t)- v_θ( y,t)\|_1≤ L_t\| x- y\|_1 for all ,,t x, y,t, where Lt≤L_t≤ L for all t. (i) Bounded Velocity Dynamics: The total time derivative of the ground-truth velocity field along any trajectory t x_t is bounded by M, i.e., ‖dt(t,t)‖1≤M \| ddt v( x_t,t) \|_1≤ M. We begin by analyzing a scenario involving a single reuse event at timestep ti+1t_i+1. Specifically, we evaluate the final error relative to the ground-truth ODE trajectory under Euler discretization. Theorem 3.2 (Global Error Bound under Cache Reuse). Under Assumption 3.1, let t x_t be the ground-truth ODE state at time t, and let ^tc x^c_t be the state generated by the Euler solver using the learned velocity θ v_θ, incorporating a single cache reuse event. Specifically, suppose that at step ti+1→tit_i+1→ t_i, we reuse a cached residual ti+1c δ_t_i+1^c with error ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with uniform step size h, the global error at the final timestep t1t_1 is bounded by: ‖t1−^t1c‖1≤hLout‖ϵti+1c‖1e(i−1)hL⏟Cache Reuse Error+(ηL+hM2L)(e(N−1)hL−1)⏟Approximation & Discretization Error. \| x_t_1- x^c_t_1 \|_1≤ hL_out \| ε^c_t_i+1 \|_1e^(i-1)hL_Cache Reuse Error+ ( ηL+ hM2L ) (e^(N-1)hL-1 )_Approximation \& Discretization Error. (11) Theorem 3.2 demonstrates that the final error can be decomposed into three distinct components: (i) the propagated error originating from cache reuse, (i) the network approximation error stemming from the learned velocity, and (i) the discretization error inherent to the ODE solver. Notably, the cache reuse term is scaled by an exponential factor, indicating that local errors introduced by cache reuse are amplified by the system dynamics as the trajectory evolves. This suggests that the impact of cache reuse should not be judged solely by the magnitude of the local error ϵti+1c ε_t_i+1^c, but rather by its “positional” impact: errors introduced earlier in the denoising process (larger i) may lead to significantly larger deviations in the final generated sample. This theoretical insight corroborates the empirical observations presented in Figure 2. In practice, we are primarily concerned with the deviation of the cached trajectory from the baseline discretization rather than from the ideal ODE solution. Our objective is to enhance the efficiency of diffusion sampling while preserving its generative fidelity as faithfully as possible. To this end, we establish error propagation bounds for single- and multi-step cache reuse in the following theorems. Theorem 3.3 (Error Propagation Bound under Single-Step Cache Reuse). Under Assumption 3.1, let ^t x_t be the state generated by the Euler solver using the learned velocity θ v_θ, and let ^tc x_t^c be the state incorporating a single cache reuse event at step ti+1→tit_i+1→ t_i. Suppose the reuse of a cached residual ti+1c δ_t_i+1^c introduces an error ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with step sizes htn+1=tn+1−tnh_t_n+1=t_n+1-t_n, the cumulative error at the final timestep t1t_1 is bounded by: ‖^t1−^t1c‖1≤‖ϵti+1c‖1ewti+1, \| x_t_1- x^c_t_1 \|_1≤ \| ε^c_t_i+1 \|_1e^w_t_i+1, (12) where the propagation exponent wti+1w_t_i+1 is defined as: wti+1=ln⁡(hti+1Lout)+∑n=1i−1htn+1Ltn+1.w_t_i+1= (h_t_i+1L_out )+ _n=1^i-1h_t_n+1L_t_n+1. (13) Theorem 3.4 (Error Propagation Bound under Multi-Step Cache Reuse). Under Assumption 3.1, let ^t x_t be the state generated by the Euler solver using the learned velocity θ v_θ, and let ^tc x_t^c be the state incorporating multiple cache reuse events at every step ti+1→tit_i+1→ t_i for i∈N−1,…,1i∈\N-1,…,1\. Suppose each reuse of a cached residual introduces a local error ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with step sizes hti+1=ti+1−tih_t_i+1=t_i+1-t_i, the cumulative error at the final timestep t1t_1 is bounded by: ‖^t1−^t1c‖1≤∑i=1N−1‖ϵti+1c‖1ewti+1. \| x_t_1- x^c_t_1 \|_1≤ _i=1^N-1 \| ε^c_t_i+1 \|_1e^w_t_i+1. (14) where the propagation exponent wtn+1w_t_n+1 is defined as: wti+1=ln⁡(hti+1Lout)+∑j=1i−1htj+1Ltj+1.w_t_i+1= (h_t_i+1L_out )+ _j=1^i-1h_t_j+1L_t_j+1. (15) Theorem 3.3 and Theorem 3.4 provide an analytical characterization of how a cached trajectory deviates from the baseline discretization. Crucially, these bounds suggest that an optimal cache reuse policy m can be identified by minimizing the upper bound of the total propagation error: ⋆()∈arg⁡min∈∑i=1N−1‖ϵti+1c‖1ewti+1, m ( s)∈ m _i=1^N-1 \| ε^c_t_i+1 \|_1e^w_t_i+1, (16) where =:‖0=KC=\ m:\| m\|_0=K\ denotes the feasible set of policies under a predefined budget K, representing the number of full-computation steps allowed throughout the denoising process. (a) Comparison of different cache policies. (b) Comparison of error propagation estimations Figure 3: Analysis of cache policies and error estimation. (a) Policy comparison. Reconstruction error across the denoising process. The theoretical policy (orange) is overly pessimistic in early stages, leading to late-stage error spikes; GCache (green) balances computation to achieve the lowest final error. (b) Estimation fidelity. Comparison of error propagation profiles. The analytical bound (red) provides a conservative upper limit, while GCache’s optimized weighting (green) aligns tightly with the empirical ground truth (blue). Effectiveness of the Analytical Upper Bound. By directly minimizing the analytical upper bound in Equation 16, we derive a cache reuse policy that accounts for the cumulative impact of errors across the entire trajectory. As illustrated in Figure 3(a), the policy optimized via this theoretical bound (Orange) consistently achieves a lower reconstruction error ‖t1−^t1‖1\| x_t_1- x_t_1\|_1 under a fixed computation budget (K=10K=10) at the final timestep compared to the state-of-the-art ERTACache [21] (Blue). This superiority stems from our bound’s ability to capture the long-term dependency of errors, whereas prior methods often rely on local heuristics that fail to account for the exponential amplification of early-stage perturbations. 3.3 Optimized Cache Reuse Policy From Theoretical Bounds to Empirical Alignment. While the policy derived from Equation 16 effectively minimizes the cumulative error, it exhibits a distinct behavior of prioritizing full computation in early denoising stages and clustering cache reuse toward the end. To understand the underlying mechanics, we analyze the discrepancy between our analytical bound and the actual empirical error. As illustrated in Figure 3(b), the analytical bound provides a conservative overestimation of the propagated error, particularly during the initial steps. This gap stems from the fact that the theoretical bound assumes a worst-case error growth, which does not fully account for the intrinsic error-resilience and non-linear dynamics of diffusion models. Motivated by this observation, we move beyond a conservative bound and introduce a bilevel optimization formulation. This approach adaptively “tightens” the error estimation by learning a weighting function that aligns our theoretical framework with empirical generation quality, ultimately yielding a more refined and effective cache reuse policy. Bilevel Optimization Formulation. To address the gap of the analytical bound discussed above, we propose Global-Impact Cache (GCache). The key idea is to move beyond a conservative upper bound by optimizing a parameterized error-weighting function that better aligns with empirical results. Specifically, we parameterize the propagation exponent wtw_t using the d-th degree Bernstein polynomials as follows: w⁡(t,)=∑ν=0dν+1(nν)tν(1−t)d−ν,w(t; s)= _ν=0^d s_ν+1 nνt^ν(1-t)^d-ν, (17) where ∈[smin,smax]d+1 s∈[s_min,s_max]^d+1 denotes a vector of learnable parameters (coefficients). With this parameterization, the search for an optimal cache reuse policy can be formulated as a bilevel optimization problem: s =arg⁡min∈[smin,smax]d+1ℒ(⋆()), = s∈[s_min,s_max]^d+1 \,L( m ( s)), (18) s.t.⋆() .t. m ( s) =arg⁡min∈∑i=1N−1‖ϵti+1c‖1ew⁡(ti+1,). = m _i=1^N-1 \| ε^c_t_i+1 \|_1e^w(t_i+1; s). (19) Here, =:‖0=KC=\ m:\| m\|_0=K\ denotes the feasible set for the policy m under a predefined budget constraint K. Intuitively, the inner objective (19) seeks an optimal cache reuse policy ⋆ m that minimizes the current upper bound of the propagated error induced by the given polynomial parameters s; while the outer objective (18) optimizes the parameters s to minimize a generation quality metric ℒL (e.g., LPIPS [34]), effectively tuning the error-weighting function to better reflect empirical generation quality. However, standard first-order methods (e.g., SGD) are inapplicable to this problem, as neither objective is differentiable with respect to s or m. We therefore develop tailored strategies for both levels. Inner Optimization via Dynamic Programming. The inner problem (19) can be cast as a constrained shortest path problem on a directed acyclic graph. We define a cost matrix E∈ℝN×NE ^N× N, where each entry Ei,j=‖ti−tj‖1ew⁡(tj,),E_i,j= \| δ_t_i- δ_t_j \|_1e^w(t_j; s), (20) quantifies the propagated error of reusing the residual from tit_i at step tjt_j. Finding the optimal policy ⋆ m is equivalent to finding a path from tNt_N to t1t_1 that minimizes cumulative cost with exactly K refresh nodes. This admits an efficient Dynamic Programming (DP) solution with O⁡(KN2)O(KN^2) complexity. Given N≤100N≤ 100 in modern schedulers, this overhead is negligible. Outer Optimization via Bayesian Optimization. Since evaluating the outer objective ℒ(⋆())L( m ( s)) requires a full inference pass over the training set, it is a high-cost black-box function. We employ Bayesian Optimization (BO) to efficiently search the parameter space of s. BO models the objective feval()=ℒ⁡(⋆())f_eval( s)=L( m ( s)) using a Gaussian Process (GP) surrogate. Let n=(i,yi)i=1nD_n=\( s_i,y_i)\_i=1^n be the history of n evaluations. The GP provides a posterior predictive distribution p⁡(y∣,,)∼⁡(μ⁡(),σ2())p(y s, S, Y) (μ( s),σ^2( s)), where the mean μ⁡()μ( s) estimates performance and the variance σ2()σ^2( s) quantifies uncertainty: μ⁡() μ( s) =⁡(,)(+σϵ2)−1, = k( s, S) ( K+ _ε^2I )^-1 Y, (21) σ2() σ^2( s) =k⁡(,)−⁡(,)(+σϵ2)−1(,)⊤. =k( s, s)- k( s, S) ( K+ _ε^2I )^-1 k( s, S) . (22) Here, =[1,2,⋯,n]⊤ S=[ s_1, s_2,·s, s_n] are reviously sampled parameters and =[y1,y2,⋯,yn]⊤ Y=[y_1,y_2,·s,y_n] are their corresponding empirical evaluations. We use the Lower Confidence Bound (LCB) [28] as the acquisition function: ALCB(,n)=μ⁡()−κnσ(),A_LCB( s;D_n)=μ( s)- _nσ( s), (23) where κn _n balances exploitation and exploration. This framework allows GCache to iteratively discover the optimal propagation exponent that best aligns the theoretical bound with empirical performance. Detailed implementation specifics for Dynamic Programming and Bayesian Optimization are deferred to Appendix A.1 and Appendix A.2, respectively. Additionally, a thorough discussion regarding the selection of our optimization objective is provided in Appendix A.3. 4 Experiments 4.1 Experimental Settings We conduct experiments on four representative DiT-based diffusion models to validate the generality and effectiveness of our method across both video and image generation. Specifically, we evaluate three video diffusion backbones, Open-Sora 1.2 [37], CogVideoX [32], and Wan 2.1 [30], as well as one strong text-to-image model, Flux-dev 1.0 [11]. Unless otherwise specified, all experiments are conducted on a single NVIDIA A800 80GB GPU, and results are reported by averaging over five random seeds. Additional experimental details are provided in Appendix D, respectively. Baselines. We compare against several recent diffusion acceleration baselines, including Δ -DiT [5], T-GATE [15], PAB [36], ProfilingDiT [18], FasterCache [17], TeaCache [14], and ERTACache [21]. Evaluation Metrics. Following prior work [14, 21], we evaluate video generation using the official 946 prompts provided by VBench [10], and image generation using the official 30K prompts from COCO [12]. For efficiency, we measure end-to-end inference latency, from prompt ingestion to the generation of the final frame, and report speedup relative to the corresponding base model. For quality, we adopt four widely used metrics: VBench [10], LPIPS [34], PSNR, and SSIM. More details are provided in Appendix D.2. 4.2 Main Results Table 1: Quantitative evaluation of efficiency and visual quality for video generation across different methods on three leading text-to-video diffusion models. Bold denotes the best performance under similar acceleration ratios. ↑ indicates higher is better, and ↓ indicates lower is better. Model Method Efficiency Visual Quality Speedup↑ Latency (s)↓ VBench↑ LPIPS↓ SSIM↑ PSNR↑ Open-Sora 1.2 (51 frames, 480P) Open-Sora 1.2 (T=30T=30) 1× 44.56 79.22% - - - Δ -DiT [5] 1.03× - 78.21% 0.5692 0.4811 11.91 T-GATE [15] 1.19× - 77.61% 0.3495 0.6760 15.50 PAB-slow [36] 1.33× 33.40 77.64% 0.1471 0.8405 24.50 PAB-fast [36] 1.40× 31.85 76.95% 0.1743 0.8220 23.58 TeaCache-slow [14] 1.55× 28.78 79.28% 0.1316 0.8415 23.62 TeaCache-fast [14] 2.25× 19.84 78.48% 0.2511 0.7477 19.10 ERTACache-slow [21] 1.55× 28.75 79.36% 0.1006 0.8706 25.45 ERTACache-fast [21] 2.47× 18.04 78.64% 0.1659 0.8170 22.34 GCache-slow (K=18K=18) 1.56× 28.54 79.48% 0.0509 0.9247 31.52 GCache-fast (K=11K=11) 2.54× 17.48 78.44% 0.1363 0.8428 24.92 CogVideoX-2B (48 frames, 480P) CogVideoX-2B (T=50T=50) 1× 78.48 80.18% - - - Δ -DiT [5] 1.26× 62.50 79.09% 0.4053 0.6126 16.15 PAB [36] 1.35× 57.98 79.76% 0.0860 0.8978 28.04 FasterCache [17] 1.62× 48.44 79.83% 0.0766 0.9066 28.93 TeaCache [14] 2.92× 26.88 79.00% 0.2057 0.7614 20.97 ERTACache-slow [21] 1.62× 48.44 79.30% 0.0368 0.9394 32.77 ERTACache-fast [21] 2.93× 26.78 78.79% 0.1012 0.8702 26.44 GCache-slow (K=31K=31) 1.62× 48.40 79.36% 0.0178 0.9647 37.53 GCache-fast (K=17K=17) 2.93× 26.76 78.30% 0.0721 0.9042 29.14 Wan2.1-1.3B (81 frames, 480P) Wan2.1-1.3B (T=50T=50) 1× 199 81.30% - - - TeaCache [14] 2.00× 99.5 76.04% 0.2913 0.5685 16.17 ProfilingDiT [18] 2.01× 99 76.15% 0.1256 0.7899 22.02 ERTACache [21] 2.17× 91.7 80.73% 0.1095 0.8200 23.77 GCache-slow (K=24K=24) 2.17× 91.6 80.81% 0.0316 0.9475 32.44 GCache-fast (K=16K=16) 3.01× 66.1 79.86% 0.0828 0.8854 22.06 Table 2: Quantitative evaluation of efficiency and visual quality for image generation across different methods on Flux-dev 1.0. Bold denotes the best performance under similar acceleration ratios. ↑ indicates higher is better, and ↓ indicates lower is better. Method Efficiency Visual Quality Speedup↑ Latency (s)↓ LPIPS↓ SSIM ↑ PSNR ↑ Flux-dev 1.0 (T=30T=30) 1× 15.96 - - - TeaCache [14] 2.84× 5.62 0.4427 0.7445 16.48 ERTACache [21] 2.87× 5.56 0.2658 0.7863 20.60 GCache-slow (K=14K=14) 2.05× 7.78 0.0900 0.9129 28.50 GCache-fast (K=10K=10) 2.87× 5.56 0.1825 0.8423 23.76 Figure 4: Qualitative comparison of video generation results on Wan 2.1. GCache consistently preserves higher alignment with the original, while ERTACache exhibits noticeable object and motion misalignment. Red boxes highlight object misalignment, and blue boxes indicate motion misalignment. Best viewed when zoomed in. Quantitative Evaluation. Across all evaluated settings, GCache consistently achieves state-of-the-art performance, delivering both faster inference and higher generation quality than existing cache-based acceleration methods. As shown in Table 1, GCache-Slow consistently outperforms the strongest baseline, ERTACache, across all video backbones, achieving higher VBench scores and reducing LPIPS by over 50%50\% on average while maintaining comparable acceleration. Notably, on Wan 2.1, GCache-Slow reduces LPIPS from 0.10950.1095 to 0.03160.0316 under the same 2.17×2.17× speedup, while GCache-Fast further achieves a 3.01×3.01× speedup and still surpasses ERTACache in generation quality (0.08280.0828 vs. 0.10950.1095 LPIPS). Similarly, on Flux-dev 1.0 (Table 2), GCache achieves an LPIPS of 0.18250.1825 under a 2.87×2.87× speedup setting, significantly outperforming prior methods. These results highlight a key distinction between GCache and prior cache-based methods. While methods such as ERTACache explicitly introduce additional error estimation and rectification mechanisms to compensate for reuse-induced approximation errors, GCache focuses directly on optimizing the cache reuse policy itself from a global-impact perspective. By allocating computation to the timesteps that most influence final generation quality, GCache achieves superior speed–quality trade-offs without introducing any additional inference-time computation. Qualitative Comparison. Figure 4 shows video generation results on WAN 2.1. Obviously, ERTACache suffers from motion and object misalignment under aggressive cache reuse, including misaligned motion dynamics (e.g., panda face motion) and object-level deviations (e.g., items on the table) from the original outputs. In contrast, GCache preserves consistent motion patterns and object semantics. Similarly, Figure 5 presents image generation results on Flux-dev 1.0. ERTACache exhibits clear semantic and spatial misalignment under the same prompts, such as generating four smoking stacks when the prompt specifies two, as well as malformed human structures and incorrect object relationships. By contrast, GCache maintains semantic correctness and spatial coherence, closely matching the original model outputs. Additional results and discussions are provided in Appendix F. Table 3: Ablation study on polynomial order d. d LPIPS↓ SSIM↑ PSNR↑ 11 0.1114 0.8591 26.15 22 0.0733 0.9042 29.09 33 0.0721 0.9042 29.14 44 0.0733 0.9016 28.84 Table 4: Ablation study on the outer objective ℒL. Objective LPIPS ↓ SSIM ↑ PSNR ↑ LPIPS 0.0733 0.9016 28.84 SSIM 0.0736 0.9045 29.10 LPIPS+SSIM 0.0721 0.9042 29.14 Figure 5: Qualitative comparison of image generation results on Flux-dev 1.0. Best viewed when zoomed in. 4.3 Ablation Studies and Empirical Analysis Ablation Study on Poly Degree d. We study the effect of the polynomial degree d used in Eq. 17 for modeling the propagation exponent wtw_t. Specifically, we evaluate different choices of d under a fixed budget K=17K=17 on CogVideoX-2B. As shown in Table 4, the best performance is achieved at d=3d=3, yielding the lowest LPIPS and the highest SSIM and PSNR. Therefore, we set d=3d=3 as the default choice in all experiments. Impact of the Outer Objective ℒL. To investigate the sensitivity of GCache to the choice of the outer objective, we evaluate three loss formulations on CogVideoX-2B (K=17K=17): LPIPS, SSIM, and a hybrid LPIPS+SSIM objective. As summarized in Table 4, while individual losses focus on specific image attributes (LPIPS on perceptual features and SSIM on structural integrity), their combination (LPIPS+SSIM) yields the best overall performance across all metrics. Specifically, the hybrid objective achieves the lowest LPIPS (0.0721) and the highest PSNR (29.14), suggesting that a multi-faceted supervision signal is crucial for optimizing the reuse policy. Additional Experimental Results. We provide more comprehensive evaluations and empirical studies in Appendix E. These include: (i) extensive robustness tests across diverse prompt distributions and spatial resolutions (Appendix E.1 and E.2); and (i) a detailed validation of the learned policy’s effectiveness and the fidelity of our pre-computed error proxy (Appendix E.3 and E.4). These results further substantiate the stability and generalization of GCache across various scenarios. 5 Conclusion In this paper, we first identify the misalignment between local reuse discrepancies and global generation error, establishing a formal theoretical characterization of error propagation dynamics in cache-based acceleration. 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Appendix Contents 1 Introduction 2 Preliminaries 2.1 Diffusion Models 2.2 Cache Reuse 3 Method 3.1 Motivation 3.2 Error Propagation of Cache Reuse 3.3 Optimized Cache Reuse Policy 4 Experiments 4.1 Experimental Settings 4.2 Main Results 4.3 Ablation Studies and Empirical Analysis 5 Conclusion References A Implementation Details A.1 Inner Optimization via Dynamic Programming A.2 Outer Optimization via Bayesian Optimization A.3 Optimization Objective B Proofs B.1 Proof for B.2 Proof for B.3 Proof for C Related Work C.1 Diffusion Models C.2 Diffusion Model Acceleration D Experimental Details D.1 Evaluation Prompts D.2 Evaluation Metrics D.3 Training Details D.4 Optimization Efficiency D.5 Experimental Details for Main Paper Visualizations E Additional Experiment Results E.1 Robustness to Prompt Distribution Shifts E.2 Generalization Across Resolutions E.3 Effectiveness of the Learned Policy E.4 Validation of the Pre-computed Local Error Proxy F Additional Qualitative Comparison F.1 Image Generation F.2 Vedio Generation G Limitations H Broader Impact Appendix A Implementation Details A.1 Inner Optimization via Dynamic Programming Algorithm 1 Dynamic Programming for Cache Reuse Mask Search 0: Error matrix E∈ℝN×NE ^N× N, cache refresh budget K 0: Reuse mask m∈0,1Nm∈\0,1\^N with ‖m‖0=K\|m\|_0=K 1: Define the cumulative propagated error: ℰj,i=∑τ=j+1i−1Ej,τ,0≤j<i≤NE_j,i= _τ=j+1^i-1E_j,τ, 0≤ j<i≤ N 2: Initialize DP table dp[k,i]dp[k,i] with +∞+∞ and parent table par[k,i]par[k,i] with −1-1 for all k,ik,i 3: dp[1,0]←0dp[1,0]← 0 4: for k=2,…,Kk=2,…,K do 5: for i=k−1,…,N−1i=k-1,…,N-1 do 6: dp[k,i]←min0≤j<i⁡(dp[k−1,j]+ℰj,i)dp[k,i]← _0≤ j<i (dp[k-1,j]+E_j,i ) 7: par[k,i]←arg⁡min0≤j<i⁡(dp[k−1,j]+ℰj,i)par[k,i]← _0≤ j<i (dp[k-1,j]+E_j,i ) 8: end for 9: end for 10: rK←arg⁡min0≤j≤N−1⁡(dp[K,j]+ℰj,N)r_K← _0≤ j≤ N-1 (dp[K,j]+E_j,N ) 11: Construct m from r1,…,rK\r_1,…,r_K\ by backtracking using parpar 12: return m Given the propagated error matrix E defined in Eq. 20, where each entry encodes the cost incurred by reusing a cached residual across timesteps, selecting an optimal cache reuse policy amounts to minimizing the cumulative propagation error under a fixed refresh budget. Recall that a cache reuse policy can be characterized by a set of K refresh timesteps, which partition the denoising trajectory into K segments. Within each segment, intermediate timesteps reuse the most recent cached residual and accumulate the corresponding propagation costs. Consequently, the total error induced by a policy is the sum of propagation costs over all segments, which naturally leads to a shortest-path formulation. To solve this problem efficiently, we adopt a dynamic programming approach. We define the DP state dp[k,i]dp[k,i] as the minimum accumulated propagation error when the k-th cache refresh occurs at timestep i. Transitioning from a previous refresh point j<ij<i to i incurs an additional cost given by the propagated error ℰj,iE_j,i, which aggregates reuse costs between these two refresh points. The objective is then to find K refresh points that minimize the total accumulated error while satisfying the constraint ‖m‖0=K\|m\|_0=K. Algorithm 1 summarizes the resulting dynamic programming procedure, which runs in O⁡(KN2)O(KN^2) time. Since the number of denoising steps N is typically fewer than 100100 in practice, the computational overhead of this optimization is totally negligible. A.2 Outer Optimization via Bayesian Optimization Algorithm 2 Bilevel Optimization for Cache Policy Search 0: Initial observations 0=(i,yi)i=1mD_0=\( s_i,y_i)\_i=1^m, exploration parameter κn _n, total optimization step T 1: for n=0n=0 to T−1T-1 do 2: Update GP surrogate using nD_n 3: n+1=arg⁡minμ()−κnσ() s_n+1= s \,μ( s)- _nσ( s) 4: ⋆(n+1)=arg⁡min∈∑i=1N−1‖ϵti+1c‖1ew⁡(ti+1,n+1) m ( s_n+1)= m _i=1^N-1 \| ε^c_t_i+1 \|_1e^w(t_i+1; s_n+1) 5: yn+1=ℒ⁡(⋆(n+1))y_n+1=L( m ( s_n+1)) 6: n+1=n∪(n+1,yn+1)D_n+1=D_n∪\( s_n+1,y_n+1)\ 7: end for 8: Update GP surrogate using TD_T 9: ⋆=arg⁡minμ() s = s \,μ( s) 10: ⋆=arg⁡min∈∑i=1N−1‖ϵti+1c‖1ew⁡(ti+1,⋆) m = m _i=1^N-1 \| ε^c_t_i+1 \|_1e^w(t_i+1; s ) The comprehensive optimization procedure for GCache is summarized in Algorithm 2. At each iteration n+1n+1, we maintain a Gaussian Process (GP) surrogate to model the objective landscape over the parameter space s. The next candidate is identified by minimizing the Lower Confidence Bound (LCB) acquisition function, which strategically balances exploration and exploitation: n+1=arg⁡minALCB(,n). s_n+1= s \,A_LCB( s;D_n). (24) Conditioned on the proposed parameters n+1 s_n+1, the inner optimization level formulates the weighted error objective and identifies the optimal cache reuse policy ⋆(n+1) m ( s_n+1). This is achieved by minimizing the accumulated propagation error subject to the budget constraint ∈ m (Equation 16), leveraging the efficient dynamic programming solver detailed in Appendix A.1. Subsequently, we evaluate the empirical generation loss yn+1=feval(n+1)=ℒ⁡(⋆(n+1))y_n+1=f_eval( s_n+1)=L( m ( s_n+1)) to augment the observation set n+1=∪(n+1,yn+1)D_n+1=D∪\( s_n+1,y_n+1)\ and refine the GP surrogate. This iterative cycle continues until the evaluation budget is exhausted, ultimately yielding an optimized propagation exponent that aligns the analytical error bound with empirical generation quality. A.3 Optimization Objective In the outer objective of the bilevel optimization framework (Equation 18), we define the loss function ℒL to evaluate the empirical generation quality. Specifically, we utilize a joint objective that combines the Learned Perceptual Image Patch Similarity (LPIPS) [34] and the Structural Similarity Index Measure (SSIM): ℒ=ℒLPIPS+(1−ℒSSIM).L=L_LPIPS+(1-L_SSIM). (25) The rationale for this dual-component objective is twofold: • Semantic and Perceptual Fidelity: LPIPS leverages deep features from pre-trained networks (e.g., VGG or AlexNet) to quantify high-level perceptual similarity. In the context of cache-based acceleration, aggressive reuse can lead to “semantic drift” or the loss of fine-grained textures that traditional metrics often fail to capture. LPIPS ensures that the optimized caching policy preserves the overall visual intent and semantic coherence of the generated samples. • Structural and Pixel-level Integrity: While LPIPS is effective for high-level perception, it can occasionally overlook local structural misalignments. By incorporating 1−ℒSSIM1-L_SSIM, we explicitly penalize deviations in local luminance, contrast, and spatial structure. This term acts as a regularizer to ensure that the accelerated trajectory remains spatially faithful to the unperturbed baseline, preventing artifacts such as ghosting or structural blurring that may arise during the accumulation of propagation errors. To empirically justify the rationale behind our hybrid optimization objective, we conduct an ablation study comparing various loss formulations, with detailed results provided in Section 4.3. The findings corroborate that the combination of LPIPS and SSIM achieves a superior balance between perceptual fidelity and structural consistency. Appendix B Proofs B.1 Proof for Theorem 3.2 Lemma B.1 (Single-Step Propagation Error). Under Assumption 3.1, let t x_t denote the state at time t along the ground-truth ODE trajectory, and let ^t x_t be the state generated by the Euler solver using the learned velocity θ v_θ. For a backward step size hti+1=ti+1−ti>0h_t_i+1=t_i+1-t_i>0, the error at time tit_i is bounded by: ‖ti−^ti‖1≤(1+hti+1Lti+1)‖ti+1−^ti+1‖1+hti+1η+hti+122M. \| x_t_i- x_t_i \|_1≤ (1+h_t_i+1L_t_i+1 ) \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η+ h_t_i+1^22M. (26) Proof. By Taylor’s theorem, the ground-truth state ti x_t_i can be expanded about ti+1t_i+1 by: ti x_t_i =ti+1−(ti+1−ti)dtdt|ti+1+(ti+1−ti)22d2tdt2|ξi+1 = x_t_i+1-(t_i+1-t_i) . d x_tdt |_t_i+1+ . (t_i+1-t_i)^22 d^2 x_tdt^2 |_ _i+1 =ti+1−hti+1(ti+1,ti+1)+hti+122dt(t,t)|ξi+1, = x_t_i+1-h_t_i+1 v( x_t_i+1,t_i+1)+ h_t_i+1^22 . ddt v( x_t,t) |_ _i+1, (27) where ξi+1∈[ti,ti+1] _i+1∈[t_i,t_i+1] is an intermediate time point arising from the Lagrange form of the remainder, and we use the relation dtdt=⁡(t,t) d x_tdt= v( x_t,t). The Euler update for ^ti x_t_i is defined as: ^ti=^ti+1−hti+1θ(^ti+1,ti+1). x_t_i= x_t_i+1-h_t_i+1 v_θ( x_t_i+1,t_i+1). (28) Subtracting the discrete update from the continuous Taylor expansion, we obtain: ti−^ti=ti+1−^ti+1−hti+1(⁡(ti+1,ti+1)−θ(^ti+1,ti+1))+hti+122dt(t,t)|ξi+1. x_t_i- x_t_i= x_t_i+1- x_t_i+1-h_t_i+1 ( v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) )+ h_t_i+1^22 . ddt v( x_t,t) |_ _i+1. (29) To bound the difference in velocity terms, we decompose it into a propagation component and an approximation component: ⁡(ti+1,ti+1)−θ(^ti+1,ti+1) v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) =⁡(ti+1,ti+1)−θ(ti+1,ti+1)⏟Approximation Error = v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1)_Approximation Error +θ(ti+1,ti+1)−θ(^ti+1,ti+1)⏟Propagated Error. \ + v_θ( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1)_Propagated Error. (30) Taking the ℓ1 _1-norm on both sides and applying the triangle inequality yields: ‖ti−^ti‖1 \| x_t_i- x_t_i \|_1 ≤‖ti+1−^ti+1‖1 ≤ \| x_t_i+1- x_t_i+1 \|_1 +hti+1‖⁡(ti+1,ti+1)−θ(ti+1,ti+1)‖1 +h_t_i+1 \| v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) \|_1 +hti+1‖θ(ti+1,ti+1)−θ(^ti+1,ti+1)‖1 +h_t_i+1 \| v_θ( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) \|_1 +hti+122‖dt(t,t)|ξi+1‖1. + h_t_i+1^22 \| . ddt v( x_t,t) |_ _i+1 \|_1. (31) Applying the Lipschitz continuity of v (with constant Lti+1L_t_i+1), the approximation bound η, and the total derivative bound M from Assumption 3.1, we have: ‖ti−^ti‖1 \| x_t_i- x_t_i \|_1 ≤‖ti+1−^ti+1‖1+hti+1Lti+1‖ti+1−^ti+1‖1+hti+1η+hti+122M ≤ \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1L_t_i+1 \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η+ h_t_i+1^22M =(1+hti+1Lti+1)‖ti+1−^ti+1‖1+hti+1η+hti+122M, = (1+h_t_i+1L_t_i+1 ) \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η+ h_t_i+1^22M, (32) which completes the proof. ∎ Lemma B.2 (Single-Step Propagation Error under Cache Reuse). Under Assumption 3.1, let t x_t denote the state at time t along the ground-truth ODE trajectory, and let ^t x_t be the state generated by the Euler solver. Suppose that at time ti+1t_i+1, we reuse a cached residual ti+1c δ_t_i+1^c such that the reuse error is ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Let ^tic x_t_i^c be the state at tit_i produced by an Euler step from ^ti+1 x_t_i+1 using the cached velocity θc v_θ^c. For a backward step size hti+1=ti+1−ti>0h_t_i+1=t_i+1-t_i>0, the error at time tit_i is bounded by: ‖ti−^tic‖1≤(1+hti+1Lti+1)‖ti+1−^ti+1‖1+hti+1η+hti+1Lout‖ϵti+1c‖1+hti+122M. \| x_t_i- x^c_t_i \|_1≤ (1+h_t_i+1L_t_i+1 ) \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η+h_t_i+1L_out \| ε^c_t_i+1 \|_1+ h_t_i+1^22M. (33) Proof. By Taylor’s theorem, the ground-truth state ti x_t_i can be expanded about ti+1t_i+1 by: ti=ti+1−hti+1(ti+1,ti+1)+hti+122dt(t,t)|ξi+1, x_t_i= x_t_i+1-h_t_i+1 v( x_t_i+1,t_i+1)+ h_t_i+1^22 . ddt v( x_t,t) |_ _i+1, (34) where ξi+1∈[ti,ti+1] _i+1∈[t_i,t_i+1] is an intermediate time point arising from the Lagrange form of the remainder, and we use the relation dtdt=⁡(t,t) d x_tdt= v( x_t,t). Let θc(t,t) v^c_θ( x_t,t) denote the learned velocity computed using the cached residual. The Euler update with cache reuse for ^ti x_t_i is defined as: ^tic=^ti+1−hti+1θc(^ti+1,ti+1). x^c_t_i= x_t_i+1-h_t_i+1 v^c_θ( x_t_i+1,t_i+1). (35) Subtracting the discrete update from the Taylor expansion, we have: ti−^tic=ti+1−^ti+1−hti+1(⁡(ti+1,ti+1)−θc(^ti+1,ti+1))+hti+122dt(t,t)|ξi+1. x_t_i- x^c_t_i= x_t_i+1- x_t_i+1-h_t_i+1 ( v( x_t_i+1,t_i+1)- v^c_θ( x_t_i+1,t_i+1) )+ h_t_i+1^22 . ddt v( x_t,t) |_ _i+1. (36) We decompose the velocity difference into three components to isolate the cache reuse error: ⁡(ti+1,ti+1)−θc(^ti+1,ti+1) v( x_t_i+1,t_i+1)- v^c_θ( x_t_i+1,t_i+1) =⁡(ti+1,ti+1)−θ(ti+1,ti+1)⏟Approximation Error = v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1)_Approximation Error +θ(ti+1,ti+1)−θ(^ti+1,ti+1)⏟Propagated Error + v_θ( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1)_Propagated Error +θ(^ti+1,ti+1)−θc(^ti+1,ti+1)⏟Cache Reuse Error. + v_θ( x_t_i+1,t_i+1)- v^c_θ( x_t_i+1,t_i+1)_Cache Reuse Error. (37) Taking the ℓ1 _1-norm on both sides and applying the triangle inequality yields: ‖ti−^tic‖1 \| x_t_i- x^c_t_i \|_1 ≤‖ti+1−^ti+1‖1 ≤ \| x_t_i+1- x_t_i+1 \|_1 +hti+1‖⁡(ti+1,ti+1)−θ(ti+1,ti+1)‖1 +h_t_i+1 \| v( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) \|_1 +hti+1‖θ(ti+1,ti+1)−θ(^ti+1,ti+1)‖1 +h_t_i+1 \| v_θ( x_t_i+1,t_i+1)- v_θ( x_t_i+1,t_i+1) \|_1 +hti+1‖θ(^ti+1,ti+1)−θc(^ti+1,ti+1)‖1 +h_t_i+1 \| v_θ( x_t_i+1,t_i+1)- v^c_θ( x_t_i+1,t_i+1) \|_1 +hti+122‖dt(t,t)|ξi+1‖1. + h_t_i+1^22 \| . ddt v( x_t,t) |_ _i+1 \|_1. (38) Given the model architecture θ(t,t)=fout(t+t) v_θ( x_t,t)=f_out( h_t+ δ_t), where t h_t is the feature and t δ_t is the residual, the cache reuse error term is bounded by the Lipschitz constant LoutL_out: ‖fout(ti+1+ti+1)−fout(ti+1+ti+1c)‖1≤Lout‖ti+1−ti+1c‖1=Lout‖ϵti+1c‖1. \|f_out( h_t_i+1+ δ_t_i+1)-f_out( h_t_i+1+ δ^c_t_i+1) \|_1≤ L_out \| δ_t_i+1- δ^c_t_i+1 \|_1=L_out \| ε^c_t_i+1 \|_1. (39) Finally, substituting the Lipschitz constant Lti+1L_t_i+1, the approximation bound η, and the total derivative bound M from Assumption 3.1, we obtain: ‖ti−^ti‖1 \| x_t_i- x_t_i \|_1 ≤‖ti+1−^ti+1‖1+hti+1Lti+1‖ti+1−^ti+1‖1+hti+1η ≤ \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1L_t_i+1 \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η +hti+1Lout‖ϵti+1c‖1+hti+122M \ +h_t_i+1L_out \| ε^c_t_i+1 \|_1+ h_t_i+1^22M =(1+hti+1Lti+1)‖ti+1−^ti+1‖1+hti+1η = (1+h_t_i+1L_t_i+1 ) \| x_t_i+1- x_t_i+1 \|_1+h_t_i+1η +hti+1Lout‖ϵti+1c‖1+hti+122M. \ +h_t_i+1L_out \| ε^c_t_i+1 \|_1+ h_t_i+1^22M. (40) This completes the proof. ∎ Theorem 3.2 (Global Error Bound under Cache Reuse). Under Assumption 3.1, let t x_t be the ground-truth ODE state at time t, and let ^tc x^c_t be the state generated by the Euler solver using the learned velocity θ v_θ, incorporating a single cache reuse event. Specifically, suppose that at step ti+1→tit_i+1→ t_i, we reuse a cached residual ti+1c δ_t_i+1^c with error ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with uniform step size h, the global error at the final timestep t1t_1 is bounded by: ‖t1−^t1c‖1 \| x_t_1- x^c_t_1 \|_1 ≤hLout‖ϵti+1c‖1e(i−1)hL⏟Cache Reuse Error+(ηL+hM2L)(e(N−1)hL−1)⏟Approximation & Discretization Error. ≤ hL_out \| ε^c_t_i+1 \|_1e^(i-1)hL_Cache Reuse Error+ ( ηL+ hM2L ) (e^(N-1)hL-1 )_Approximation \& Discretization Error. (41) Proof. We analyze the error accumulation by recursively applying the single-step error bounds. From Lemma B.1, the error at the final timestep t1t_1 can be expressed in terms of the error at an intermediate step tit_i: ‖t1−^t1c‖1≤‖ti−^tic‖1(1+hL)i−1+(hη+h22M)∑n=1i−1(1+hL)n−1. \| x_t_1- x^c_t_1 \|_1≤ \| x_t_i- x^c_t_i \|_1(1+hL)^i-1+ (h\,η+ h^22M ) _n=1^i-1(1+hL)^n-1. (42) At the specific transition ti+1→tit_i+1→ t_i where cache reuse occurs, Lemma B.2 provides the local bound: ‖ti−^tic‖1≤(1+hL)‖ti+1−^ti+1‖1+hη+hLout‖ϵti+1c‖1+h22M. \| x_t_i- x^c_t_i \|_1≤(1+hL) \| x_t_i+1- x_t_i+1 \|_1+h\,η+hL_out \| ε^c_t_i+1 \|_1+ h^22M. (43) Continuing the recursion for the remaining steps from ti+1t_i+1 back to the initial state tNt_N, we observe that for all other steps n∈i+1,…,N−1n∈\i+1,…,N-1\, the standard local error bound from Lemma B.1 applies. Combining these, the global error at t1t_1 becomes: ‖t1−^t1c‖1≤‖tN−^tN‖1(1+hL)N−1+hLout‖ϵti+1c‖1(1+hL)i−1 \| x_t_1- x^c_t_1 \|_1≤ \| x_t_N- x_t_N \|_1 (1+hL )^N-1+h\,L_out \| ε^c_t_i+1 \|_1 (1+hL )^i-1 +(hη+h22M)∑n=1N−1(1+hL)n−1. + (h\,η+ h^22M ) _n=1^N-1(1+hL)^n-1. (44) Assuming the solver starts from the ground-truth initial noise, we have tN=^tN x_t_N= x_t_N and the first term vanishes. The remaining terms simplify to: ‖t1−^t1c‖1≤hLout‖ϵti+1c‖1(1+hL)i−1+(hη+h22M)∑n=1N−1(1+hL)n−1. \| x_t_1- x^c_t_1 \|_1≤ h\,L_out \| ε^c_t_i+1 \|_1 (1+hL )^i-1+ (h\,η+ h^22M ) _n=1^N-1(1+hL)^n-1. (45) Using the geometric series identity ∑j=0k−1rj=rk−1r−1 _j=0^k-1r^j= r^k-1r-1 with r=1+hLr=1+hL, the remaining terms simplifies to: ‖t1−^t1c‖1 \| x_t_1- x^c_t_1 \|_1 ≤hLout‖ϵti+1c‖1(1+hL)i−1+(hη+h22M)1hL((1+hL)N−1−1) ≤ hL_out \| ε^c_t_i+1 \|_1(1+hL)^i-1+ (hη+ h^22M ) 1hL ((1+hL)^N-1-1 ) =hLout‖ϵti+1c‖1(1+hL)i−1+(ηL+hM2L)((1+hL)N−1−1) =hL_out \| ε^c_t_i+1 \|_1(1+hL)^i-1+ ( ηL+ hM2L ) ((1+hL)^N-1-1 ) (46) Finally, employing the inequality 1+a≤ea1+a≤ e^a, we arrive at the final bound: ‖t1−^t1c‖1 \| x_t_1- x^c_t_1 \|_1 ≤hLout‖ϵti+1c‖1e(i−1)hL+(ηL+hM2L)(e(N−1)hL−1). ≤ hL_out \| ε^c_t_i+1 \|_1e^(i-1)hL+ ( ηL+ hM2L ) (e^(N-1)hL-1 ). (47) This completes the proof. ∎ B.2 Proof for Theorem 3.3 Theorem 3.3 (Error Propagation Bound under Single-Step Cache Reuse). Under Assumption 3.1, let ^t x_t be the state generated by the Euler solver using the learned velocity θ v_θ, and let ^tc x_t^c be the state incorporating a single cache reuse event at step ti+1→tit_i+1→ t_i. Suppose the reuse of a cached residual ti+1c δ_t_i+1^c introduces an error ϵti+1c=ti+1−ti+1c ε_t_i+1^c= δ_t_i+1- δ^c_t_i+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with step sizes htn+1=tn+1−tnh_t_n+1=t_n+1-t_n, the cumulative error at the final timestep t1t_1 is bounded by: ‖^t1−^t1c‖1≤‖ϵti+1c‖1ewti+1, \| x_t_1- x^c_t_1 \|_1≤ \| ε^c_t_i+1 \|_1e^w_t_i+1, (48) where the propagation exponent wti+1w_t_i+1 is defined as: wti+1=ln⁡(hti+1Lout)+∑n=1i−1htn+1Ltn+1.w_t_i+1= (h_t_i+1L_out )+ _n=1^i-1h_t_n+1L_t_n+1. (49) Proof. We first bound the error propagation for the steps following the cache reuse (tnt_n for n<in<i). The Euler updates for the standard and cached trajectories are: ^tn x_t_n =^tn+1−htn+1θ(^tn+1,tn+1), = x_t_n+1-h_t_n+1 v_θ( x_t_n+1,t_n+1), (50) ^tnc x^c_t_n =^tn+1c−htn+1θ(^tn+1c,tn+1). = x^c_t_n+1-h_t_n+1 v_θ( x^c_t_n+1,t_n+1). (51) Subtracting these updates and applying the triangle inequality: ‖^tn−^tnc‖1 \| x_t_n- x^c_t_n \|_1 =‖^tn+1−^tn+1c−htn+1(θ(^tn+1,tn+1)−θ(^tn+1c,tn+1))‖1 = \| x_t_n+1- x_t_n+1^c-h_t_n+1 ( v_θ( x_t_n+1,t_n+1)- v_θ( x^c_t_n+1,t_n+1) ) \|_1 ≤‖^tn+1−^tn+1c‖1+htn+1‖θ(^tn+1,tn+1)−θ(^tn+1c,tn+1)‖1 ≤ \| x_t_n+1- x_t_n+1^c \|_1+h_t_n+1 \| v_θ( x_t_n+1,t_n+1)- v_θ( x^c_t_n+1,t_n+1) \|_1 ≤(1+htn+1Ltn+1)‖^tn+1−^tn+1c‖1, ≤(1+h_t_n+1L_t_n+1) \| x_t_n+1- x_t_n+1^c \|_1, (52) where Ltn+1L_t_n+1 is the Lipschitz constant of θ v_θ. Applying this relation recursively from t1t_1 back to tit_i yields: ‖^t1−^t1c‖1≤‖^ti−^tic‖1∏n=1i−1(1+htn+1Ltn+1). \| x_t_1- x^c_t_1 \|_1≤ \| x_t_i- x^c_t_i \|_1 _n=1^i-1(1+h_t_n+1L_t_n+1). (53) Next, we bound the local error injected at step tit_i. At this step, both trajectories originate from the same state ^ti+1 x_t_i+1, but the cached trajectory uses the approximate velocity θc v^c_θ. The updates are: ^ti x_t_i =^ti+1−hti+1θ(^ti+1,ti+1), = x_t_i+1-h_t_i+1 v_θ( x_t_i+1,t_i+1), (54) ^tic x^c_t_i =^ti+1−hti+1θc(^ti+1,ti+1). = x_t_i+1-h_t_i+1 v^c_θ( x_t_i+1,t_i+1). (55) The norm of the difference is thus: ‖^ti−^tic‖1=hti+1‖θ(^ti+1,ti+1)−θc(^ti+1,ti+1)‖1. \| x_t_i- x^c_t_i \|_1=h_t_i+1 \| v_θ( x_t_i+1,t_i+1)- v^c_θ( x_t_i+1,t_i+1) \|_1. (56) Using the model architecture θ(,t)=fout(+) v_θ( x,t)=f_out( h+ δ) and the Lipschitz continuity of the output layer foutf_out, we have: ‖fout(ti+1+ti+1)−fout(ti+1+ti+1c)‖1≤Lout‖ϵti+1c‖1. \|f_out( h_t_i+1+ δ_t_i+1)-f_out( h_t_i+1+ δ^c_t_i+1) \|_1≤ L_out \| ε^c_t_i+1 \|_1. (57) Substituting this into the local error bound yields: ‖^ti−^tic‖1≤hti+1Lout‖ϵti+1c‖1. \| x_t_i- x^c_t_i \|_1≤ h_t_i+1L_out \| ε^c_t_i+1 \|_1. (58) Combining the propagation and local error bounds, and applying 1+a≤ea1+a≤ e^a: ‖^t1−^t1c‖1 \| x_t_1- x^c_t_1 \|_1 ≤hti+1Lout‖ϵti+1c‖1∏n=1i−1exp⁡(htn+1Ltn+1) ≤ h_t_i+1L_out \| ε^c_t_i+1 \|_1 _n=1^i-1 (h_t_n+1L_t_n+1) =‖ϵti+1c‖1exp⁡(ln⁡(hti+1Lout)+∑n=1i−1htn+1Ltn+1). = \| ε^c_t_i+1 \|_1 ( (h_t_i+1L_out)+ _n=1^i-1h_t_n+1L_t_n+1 ). (59) This completes the proof. ∎ B.3 Proof for Theorem 3.4 Theorem 3.4 (Error Propagation Bound under Multi-Step Cache Reuse). Under Assumption 3.1, let ^t x_t be the state generated by the Euler solver using the learned velocity θ v_θ, and let ^tc x_t^c be the state incorporating multiple cache reuse events at every step tn+1→tnt_n+1→ t_n for n∈N−1,…,1n∈\N-1,…,1\. Suppose each reuse of a cached residual introduces a local error ϵtn+1c=tn+1−tn+1c ε_t_n+1^c= δ_t_n+1- δ^c_t_n+1. Given a sequence of timesteps tN,tN−1,…,t1t_N,t_N-1,…,t_1 with step sizes htn+1=tn+1−tnh_t_n+1=t_n+1-t_n, the cumulative error at the final timestep t1t_1 is bounded by: ‖^t1−^t1c‖1≤∑n=1N−1‖ϵtn+1c‖1ewtn+1. \| x_t_1- x^c_t_1 \|_1≤ _n=1^N-1 \| ε^c_t_n+1 \|_1e^w_t_n+1. (60) where the propagation exponent wtn+1w_t_n+1 is defined as: wtn+1=ln⁡(htn+1Lout)+∑m=1n−1htm+1Ltm+1.w_t_n+1= (h_t_n+1L_out )+ _m=1^n-1h_t_m+1L_t_m+1. (61) Proof. We begin by analyzing the error transition for a single step tn+1→tnt_n+1→ t_n. The standard Euler update and the cached Euler update are given by: ^tn x_t_n =^tn+1−htn+1θ(^tn+1,tn+1), = x_t_n+1-h_t_n+1 v_θ( x_t_n+1,t_n+1), (62) ^tnc x^c_t_n =^tn+1c−htn+1θc(^tn+1c,tn+1). = x^c_t_n+1-h_t_n+1 v^c_θ( x^c_t_n+1,t_n+1). (63) Subtracting these updates, we have: ^tn−^tnc=^tn+1−^tn+1c−htn+1(θ(^tn+1,tn+1)−θc(^tn+1c,tn+1)). x_t_n- x^c_t_n= x_t_n+1- x^c_t_n+1-h_t_n+1 ( v_θ( x_t_n+1,t_n+1)- v^c_θ( x^c_t_n+1,t_n+1) ). (64) We decompose the velocity difference into two components to isolate the cache reuse error: θ(^tn+1,tn+1)−θc(^tn+1c,tn+1) v_θ( x_t_n+1,t_n+1)- v^c_θ( x^c_t_n+1,t_n+1) =θ(^tn+1,tn+1)−θ(^tn+1c,tn+1)⏟Propagated Error = v_θ( x_t_n+1,t_n+1)- v_θ( x^c_t_n+1,t_n+1)_Propagated Error +θ(^tn+1c,tn+1)−θc(^tn+1c,tn+1)⏟Cache Reuse Error. \ + v_θ( x^c_t_n+1,t_n+1)- v^c_θ( x^c_t_n+1,t_n+1)_Cache Reuse Error. (65) Applying the Lipschitz constant Ltn+1L_t_n+1 for the velocity θ v_θ and LoutL_out for the output layer foutf_out with the triangle inequality, we obtain the recurrence relation: ‖^tn−^tnc‖1 \| x_t_n- x^c_t_n \|_1 ≤‖^tn+1−^tn+1c‖1 ≤ \| x_t_n+1- x^c_t_n+1 \|_1 +htn+1‖θ(^tn+1,tn+1)−θ(^tn+1c,tn+1)‖1 +h_t_n+1 \| v_θ( x_t_n+1,t_n+1)- v_θ( x^c_t_n+1,t_n+1) \|_1 +htn+1‖θ(^tn+1c,tn+1)−θc(^tn+1c,tn+1)‖1 +h_t_n+1 \| v_θ( x^c_t_n+1,t_n+1)- v^c_θ( x^c_t_n+1,t_n+1) \|_1 (66) ≤(1+htn+1Ltn+1)‖^tn+1−^tn+1c‖1+htn+1Lout‖ϵtn+1c‖1. ≤ (1+h_t_n+1L_t_n+1 ) \| x_t_n+1- x^c_t_n+1 \|_1+h_t_n+1L_out \| ε^c_t_n+1 \|_1. (67) Applying this relation recursively from t1t_1 back to tNt_N yields: ‖^t1−^t1c‖1 \| x_t_1- x^c_t_1 \|_1 ≤‖^tN−^tNc‖1∏n=1N−1(1+htn+1Ltn+1) ≤ \| x_t_N- x^c_t_N \|_1 _n=1^N-1 (1+h_t_n+1L_t_n+1 ) +∑n=1N−1htn+1Lout‖ϵtn+1c‖1∏m=1n−1(1+htm+1Ltm+1). \ + _n=1^N-1h_t_n+1L_out \| ε^c_t_n+1 \|_1 _m=1^n-1 (1+h_t_m+1L_t_m+1 ). (68) Since both trajectories start from the same initial noise, we have ^tN=^tNc x_t_N= x^c_t_N and the first term vanishes, ‖^t1−^t1c‖1≤∑n=1N−1htn+1Lout‖ϵtn+1c‖1∏m=1n−1(1+htm+1Ltm+1). \| x_t_1- x^c_t_1 \|_1≤ _n=1^N-1h_t_n+1L_out \| ε^c_t_n+1 \|_1 _m=1^n-1 (1+h_t_m+1L_t_m+1 ). (69) Finally, using the inequality 1+a≤ea1+a≤ e^a, ‖^t1−^t1c‖1≤∑n=1N−1‖ϵtn+1c‖1exp⁡(ln⁡(htn+1Lout)+∑m=1n−1htm+1Ltm+1). \| x_t_1- x^c_t_1 \|_1≤ _n=1^N-1 \| ε^c_t_n+1 \|_1 ( (h_t_n+1L_out )+ _m=1^n-1h_t_m+1L_t_m+1 ). (70) This completes the proof. ∎ Appendix C Related Work C.1 Diffusion Models In recent years, diffusion models [9, 27, 6, 13] have emerged as a dominant paradigm in generative modeling, demonstrating remarkable performance across a wide range of visual generation tasks, including image [22, 24], video [1, 3], and multimodal synthesis [19]. Early diffusion models were primarily built upon lightweight U-Net architectures [23], which enabled stable training and strong generative fidelity through iterative denoising. Subsequent advances have significantly expanded model capacity by introducing transformer-based backbones, most notably Diffusion Transformers (DiTs) [20], which facilitate better scalability and have driven substantial progress in high-resolution and long-horizon generation, especially for video synthesis. Despite their strong generative capabilities, diffusion models remain computationally expensive at inference time. The sequential denoising process, combined with increasingly large backbones and longer generation horizons, results in slow sampling speed and high computational cost [5]. These limitations pose significant challenges for practical deployment in real-world scenarios, motivating extensive research on accelerating diffusion model inference. C.2 Diffusion Model Acceleration A large body of work has investigated accelerating diffusion model inference from different perspectives. A representative line of research focuses on improving the sampling solvers, aiming to reduce the number of denoising steps without modifying the underlying model. Classic approaches, such as DDIM [26], DPM-Solver [16], UniPC [35], etc., have demonstrated that carefully designed numerical solvers can significantly accelerate sampling. As a result, modern high-fidelity image and video generation models (e.g., Wan [30], OpenSora [37], Flux-dev 1.0 [11]) already adopt these advanced general-purpose solvers in practice. Nevertheless, despite such solver-level optimizations, tens of denoising steps are still required for high-quality generation, leading to substantial inference cost. Another direction explores distillation-based acceleration, where a compact student model is trained to mimic a large teacher diffusion model using fewer steps. While such methods can achieve impressive speedups, they typically require expensive retraining and large-scale supervision. This limitation becomes particularly pronounced for video diffusion models, where both training and distillation incur prohibitive computational overhead [31]. Model-level optimization constitutes another important category, including quantization and pruning. Quantization methods such as PTQD [8] reduce numerical precision to lower computation and memory cost, while pruning-based approaches like LD-Pruner [2] remove redundant structures from diffusion models. Although effective, these techniques often involve nontrivial engineering effort, additional calibration, or task-specific retraining, and their performance can be sensitive to model architecture and deployment settings. More recently, cache-based acceleration has emerged as a promising and complementary direction [5, 14, 21]. These methods exploit temporal redundancy in the reverse diffusion process by reusing intermediate representations or residuals across adjacent timesteps, without modifying the solver or retraining the backbone model. As such, cache-based techniques are largely orthogonal to solver design and can be seamlessly applied on top of existing solver-based samplers (e.g., DDIM/UniPC), enabling further acceleration in a plug-and-play manner. By reusing computation from previous denoising steps, cache-based approaches can substantially reduce inference cost while preserving generation quality, which is particularly attractive for large-scale and high-fidelity image and video diffusion models. Appendix D Experimental Details D.1 Evaluation Prompts For video generation, we follow prior work [14, 21] and evaluate all methods using the official 946 prompts provided by VBench [10]. These prompts cover a diverse set of content categories and motion patterns, and are designed to comprehensively assess video generation quality across multiple dimensions. For image generation, we adopt the official COCO validation set [12] and use the first 30K text prompts as commonly done in recent diffusion acceleration studies [14, 21]. The prompt list is publicly available and released on Hugging Face to facilitate reproducibility. All compared methods are evaluated on the same prompt sets to ensure a fair comparison. D.2 Evaluation Metrics We employ three evaluation metrics to assess generation quality and fidelity. • VBench [10] serves as a holistic benchmarking framework for video generative models. It utilizes a hierarchical Evaluation Dimension Suite to disentangle the multifaceted nature of “video quality” into distinct, well-defined metrics, thereby enabling a granular and objective assessment of generative performance. • LPIPS [34] quantifies perceptual similarity using deep feature representations, capturing subtle texture-level and semantic deviations. • PSNR and SSIM measure pixel-level and structure-level fidelity, respectively, between outputs produced by the accelerated sampler and those generated by the corresponding base model. D.3 Training Details In this section, we provide the technical details for the bilevel optimization process of GCache. The optimization is designed to be efficient while ensuring the generalizability of the learned propagation exponent. Dataset and Sampling Strategy. We utilize a training set consisting of 512 prompts randomly sampled from the corresponding dataset. To ensure the robustness of the learned policy and avoid overfitting, we strictly ensure that the random seeds used during training are distinct from those used in the evaluation and testing phases. During each iteration of the outer optimization, we evaluate the current caching policy using a batch size of 32 prompts to obtain a stable estimate of the perceptual loss (LPIPS and SSIM). Bayesian Optimization Configuration. We employ a Gaussian Process (GP) as the surrogate model for the outer objective. The optimization parameters and strategies are configured as follows: • Search Space: The learnable coefficients s for the Bernstein polynomial are bounded within the range [min,max]=[0,10][ s_min, s_max]=[0,10]. For our experiments, we set the polynomial degree d=3d=3, resulting in a 4-dimensional parameter space (d+1=4d+1=4). • Structured Initialization: Rather than random sampling, we initialize the GP surrogate using 16 deterministic points to ensure comprehensive coverage of the search space. Specifically, we define two representative centers 0.25,0.75\0.25,0.75\ in the normalized parameter space for each dimension and generate the initial set via a Cartesian product across all 4 dimensions (24=162^4=16). These normalized coordinates are then linearly mapped to the actual range [0,10][0,10]. This symmetric grid initialization ensures that the GP begins with a well-distributed understanding of the objective landscape across different quadrants. • Optimization Steps: The total optimization budget is set to 500 steps. • Exploration-Exploitation Trade-off: We utilize the Lower Confidence Bound (LCB) acquisition function: ALCB()=μ⁡()−κσ()A_LCB(s)=μ(s)-κσ(s). The exploration parameter κ is scheduled to decay linearly from 2.576 to 1.0 over the course of training. This encourages the optimizer to prioritize global exploration in early iterations and transition towards local exploitation of identified high-quality regions in the later stages. Efficient Error Pre-calculation. To minimize the computational overhead during the bilevel optimization, we implement an efficient evaluation strategy for the inner objective. Specifically, we pre-calculate the local approximation errors ϵi+1c ε^c_i+1 across 128 representative samples before the start of the optimization. Since the inner objective (the Dynamic Programming solver) only requires the magnitude of these local errors to calculate the total propagated error ∑‖ϵ‖1ew⁡(t,)Σ\|ε\|_1e^w(t; s), pre-storing these values allows the optimization process to bypass redundant model evaluations. During each step of the bilevel search, we simply scale the stored error values by the updated propagation exponent ew⁡(t,)e^w(t; s). This decoupling of error measurement from policy search significantly accelerates the optimization, reducing the search time from hours to minutes on a single GPU. Furthermore, to verify the fidelity of these pre-computed proxies, we evaluate the alignment between errors from the original and cache-reused trajectories in Appendix E.4. The results justify the use of pre-computed errors as a reliable and high-fidelity proxy for policy optimization. D.4 Optimization Efficiency Table 5: We report the budget K and the wall-clock time required. All policies were optimized in less than 24 hours, demonstrating the high efficiency of GCache. Model GPU Config Budget (K) Time Cost (hours) OpenSora 1.2 4 × H100 18 17 11 12.5 CogVideoX-2B 4 × H100 31 7 17 5 Wan2.1-1.3B 8 × H100 24 17.5 16 13.5 Flux-dev 1.0 4 × H100 14 6 10 5 Table 5 reports the optimization time and associated budgets for GCache across different architectures. Experiments were performed using 4 × H100 GPUs for most models, with 8 × H100 GPUs reserved for Wan2.1-1.3B. Crucially, GCache demonstrates remarkable efficiency: even for the most computationally demanding backbones, the optimization is finalized in less than a day. This minimal overhead makes our approach highly scalable and suitable for the rapid deployment of new diffusion backbones. D.5 Experimental Details for Main Paper Visualizations In this section, we provide the specific experimental configurations used to generate the visualizations in the main manuscript: • Figure 1: Results are evaluated using the Flux-dev 1.0 [11] backbone. Metrics are averaged over 32 randomly sampled prompts from the COCO [12] validation set. • Figure 2: The error propagation analyses are derived from CogVideoX-2B [32], with results averaged across 32 representative prompts from the VBench [10] suite. • Figure 3: The policy comparison study is conducted on Flux-dev 1.0 [11], utilizing 32 random prompts from the COCO [12] validation set for statistical consistency. Appendix E Additional Experiment Results E.1 Robustness to Prompt Distribution Shifts To evaluate the generalization capability of GCache under distribution shifts, we investigate whether a policy optimized on a specific prompt characteristic (e.g., static scenes) can generalize to others (e.g., highly dynamic videos). Using VBench [10] as a base, we curate two distinct subsets: • Static Prompts: Scenes with minimal temporal evolution, identified by keywords such as “in a still frame”, “a tranquil tableau”, “frozen in time”, “static view.” • Dynamic Prompts: Motion-intensive sequences sampled from VBench’s motion-related dimensions, including human action, dynamic degree, motion smoothness, and subject consistency. We optimize GCache on three training distributions: Static, Dynamic, and a Mixed (Random) set, and evaluate their cross-distribution performance. All of the experiments are conducted on CogVideoX-2B with K=17K=17. Table 6: Cross-distribution generalization analysis. We evaluate GCache policies optimized on different prompt subsets (Static vs. Dynamic). The negligible performance gap across training distributions demonstrates the robust generalization of our learned policy. Test Set Train Source LPIPS↓ SSIM↑ PSNR↑ Static Mixed 0.0594 0.9122 30.25 Static 0.0595 0.9118 30.26 Dynamic 0.0611 0.9109 30.26 Dynamic Mixed 0.0905 0.8982 28.04 Static 0.0905 0.8981 28.06 Dynamic 0.0921 0.8975 27.90 As shown in Table 6, the performance variance across different training sources is remarkably marginal. For instance, a policy trained on static prompts performs almost identically to one trained on dynamic prompts when tested on dynamic sequences (0.0905 vs. 0.0921 LPIPS). This high degree of stability suggests that GCache captures fundamental structural redundancies within the diffusion process that are invariant to specific prompt semantics or motion levels, ensuring its robustness for diverse real-world applications. E.2 Generalization Across Resolutions To assess the spatial scalability of GCache, we evaluate the transferability of a policy optimized at a fixed resolution to unseen spatial scales. Specifically, we apply the GCache-fast policy, originally optimized for 1024×10241024× 1024 resolution on Flux-dev 1.0 [11], directly to 512×512512× 512 and 256×256256× 256 settings without any further re-tuning or adaptation. Table 7: Zero-shot generalization across resolutions. We evaluate the GCache-fast policy (optimized at 1024×10241024× 1024) on lower resolutions (512512 and 256256) without re-tuning. GCache-fast consistently outperforms ERTACache across all scales, demonstrating its robustness to spatial resolution shifts. Resolution Method LPIPS↓ SSIM↑ PSNR↑ 1024 ERTACache 0.2658 0.7863 20.60 GCache-fast 0.1825 0.8423 23.76 512 ERTACache 0.2359 0.7580 19.97 GCache-fast 0.1514 0.8344 23.47 256 ERTACache 0.2047 0.7209 19.70 GCache-fast 0.1558 0.7746 21.74 As shown in Table 7, GCache-fast consistently outperforms the baseline ERTACache [21] by a significant margin across all tested resolutions. Notably, the performance gain remains robust even when the resolution is quadrupled (256→1024256→ 1024), underscoring that GCache captures resolution-agnostic redundancy patterns within the diffusion backbone. This zero-shot transfer capability is highly desirable for practical deployment, as it eliminates the need for resolution-specific optimization. E.3 Effectiveness of the Learned Policy A key question is whether GCache’s performance gains stem from a superior reuse policy or simply from different computational budgets. Some existing methods, such as ERTACache [21], employ an auxiliary light-weight model to rectify the errors introduced by cache reuse. To ensure a fair comparison and isolate the impact of the policy itself, we evaluate GCache against two variants of ERTACache under identical budget K: (1) ERTACache, the full version with its Time Adjustment and Error Rectification modules; and (2) ERTACache*, a stripped-down version that excludes these additional modules, relying solely on its default reuse policy. Table 8: Policy comparison under identical budget K. We compare GCache with ERTACache and its variant ERTACache* (without the error rectification module). GCache consistently achieves superior performance without requiring any auxiliary corrector models. Model K Method LPIPS↓ SSIM↑ PSNR↑ OpenSora 1.2 12 ERTACache* 0.2198 0.7648 20.24 ERTACache 0.1659 0.8170 22.34 GCache 0.1188 0.8569 25.73 CogVideoX-2B 17 ERTACache* 0.1090 0.8687 26.54 ERTACache 0.1012 0.8702 26.44 GCache 0.0721 0.9042 29.14 As summarized in Table 8, GCache consistently outperforms both variants by a significant margin across multiple backbones. Notably, GCache achieves substantially better LPIPS and PSNR than the full ERTACache, despite not using any extra corrector models. For instance, on OpenSora 1.2, GCache improves PSNR from 22.34 to 25.73. These results demonstrate that GCache’s optimization-based approach discovers a much more effective reuse trajectory, proving that a well-optimized policy can be more powerful than a sub-optimal policy supplemented by error correction. E.4 Validation of the Pre-computed Local Error Proxy As discussed in Section D.3, to circumvent the prohibitive computational overhead of generating online trajectories during optimization, GCache utilizes a pre-computed error matrix Ei,j=‖ti−tj‖1E_i,j=\| δ_t_i- δ_t_j\|_1 derived from the original (full-step) diffusion trajectory. However, a potential concern is trajectory drift: as cache reuse is introduced, the intermediate latent states may deviate from the original path, potentially rendering the pre-computed errors inaccurate. To investigate the fidelity of this approximation, we conduct an empirical study on CogVideoX-2B (K=17K=17). We compare the local residual error, defined as ‖c−ti‖1\| δ^c- δ_t_i\|_1, where ti δ_t_i is the ground-truth residual at timestep tit_i. We calculate this error under two settings: (1) the Original Trajectory, where c δ^c is sampled from the full-step inference; and (2) the Cache-reused Trajectory, where c δ^c is sampled from an actual inference process governed by our learned GCache policy. Figure 6: Validation of the pre-computed error proxy. We compare the L1 residual error ‖c−ti‖1\| δ^c- δ_t_i\|_1 during the denoising process on CogVideoX-2B (K=17K=17). The Pre-compute (red) curve denotes the error calculated from the original trajectory, while the Cache (blue) curve represents the actual error in a trajectory with GCache reuse. The “sawtooth” peaks correspond to the K cache refresh points. The high degree of overlap between the two curves justifies the use of pre-computed error E as a high-fidelity and efficient proxy for optimization. The results are visualized in Figure 6. As shown, the error profiles of the two trajectories are remarkably aligned across the entire denoising process. The “sawtooth” pattern reflects the periodic refreshing of the cache, where the error peaks just before a cache update and drops to zero immediately after. Crucially, the mean and variance of the errors in the cache-reused trajectory (blue) closely track those of the pre-computed proxy (red), even in the late stages of denoising where drift is typically most pronounced. This high degree of alignment justifies the use of pre-computed errors as a reliable and efficient proxy for optimization, as it accurately reflects the error dynamics of the actual inference process. Appendix F Additional Qualitative Comparison We provide additional qualitative results for both image and video generation. F.1 Image Generation For image generation, Figure 7 presents additional qualitative comparisons on Flux-dev 1.0. Under the same acceleration setting, ERTACache introduces various visual degradations, including background misalignment, incorrect spatial relationships between objects and subjects, missing or distorted materials, and semantic artifacts such as erroneous objects (e.g., incorrect traffic signs) and physically implausible details (e.g., airplanes depicted mid-air with landing gear deployed). By contrast, GCache remains highly faithful to the original model outputs, preserving semantic correctness, spatial coherence, and fine-grained visual details even under a 2.87×2.87× speedup setting. F.2 Vedio Generation For video generation, we provide additional qualitative comparisons across three representative text-to-video diffusion models, including CogVideoX-2B (Figure 8), Open-Sora 1.2 (Figure 9), and Wan 2.1-1.3B (Figure 10). For each example, we uniformly sample six frames from the generated video sequence to visualize temporal consistency and structural fidelity over time. Within each group, we compare outputs from ERTACache, GCache, and the ground-truth full-step original generation. Across all three models and diverse prompts, GCache consistently produces videos that remain highly faithful to the ground-truth outputs, preserving semantic correctness, object structure, and temporal coherence throughout the sequence. The generated contents exhibit stable object appearances and natural motion transitions, with minimal degradation under accelerated sampling. In contrast, ERTACache frequently introduces noticeable visual artifacts and semantic inconsistencies. Typical failure cases include distorted object geometry (e.g., malformed cups, umbrellas, and sharks), incorrect semantic structures (e.g., unrealistic astronaut body configurations), and unstable object appearances across frames. These artifacts become more evident in dynamic scenes and complex compositions, indicating weaker preservation of global semantic information. Overall, the qualitative results further demonstrate that GCache achieves substantially better fidelity and temporal consistency under the same acceleration budget. Appendix G Limitations Although GCache effectively optimizes cache policies, it currently operates under a fixed refresh budget and relies on pre-computed error proxies, which may not fully account for dynamic input complexity or extreme trajectory shifts. Future work could explore sample-adaptive scheduling and more diverse perceptual objectives to further enhance temporal consistency in highly dynamic videos. Appendix H Broader Impact By substantially reducing the computational cost of large-scale diffusion models, GCache promotes environmental sustainability and democratizes access to state-of-the-art generative tools for users with limited hardware resources. While accelerated generation could potentially be misused for creating synthetic misinformation, we advocate for its deployment alongside robust safety filters and digital watermarking technologies to mitigate such risks. Figure 7: Additional qualitative comparison results for image generation on Flux-dev 1.0. Best viewed zoomed in. ERTACache GCache Ground Truth (a) A cup and a couch. ERTACache GCache Ground Truth (b) An astronaut flying in space, in super slow motion. ERTACache GCache Ground Truth (c) Fireworks. ERTACache GCache Ground Truth (d) A beautiful coastal beach in spring, waves lapping on sand, racking focus. Figure 8: Temporal consistency comparison on CogVideoX-2B. Each group visualizes six evenly spaced frames from the generated sequence. ERTACache GCache Ground Truth (a) Gwen Stacy reading a book, in cyberpunk style. ERTACache GCache Ground Truth (b) a cell phone. ERTACache GCache Ground Truth (c) A couple in formal evening wear going home get caught in a heavy downpour with umbrellas, in super slow motion. ERTACache GCache Ground Truth (d) a shark is swimming in the ocean, oil painting Figure 9: Temporal consistency comparison on Open-Sora 1.2. Each group visualizes six evenly spaced frames from the generated sequence. ERTACache GCache Ground Truth (a) A bear climbing a tree. ERTACache GCache Ground Truth (b) A panda drinking coffee in a cafe in Paris, pan left. ERTACache GCache Ground Truth (c) A tranquil tableau of bathroom. ERTACache GCache Ground Truth (d) Skis and a snowboard. Figure 10: Temporal consistency comparison on Wan 2.1-1.3B. Each group visualizes six evenly spaced frames from the generated sequence.

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