jiajianxie-ComfyUI-AccelDiff/docs/zeus.md

ZEUS

Category: Sampler-level acceleration

Overview

ZEUS is an acceleration method that predicts reduced denoiser evaluations using a second-order predictor, and stabilizes aggressive consecutive skipping with an interleaved scheme that avoids back-to-back extrapolations. ZEUS adds essentially zero overhead, no feature caches, and no architectural modifications, and it is compatible with different backbones, prediction objectives, and solver choices.

Parameters

Parameter	Type	Default	Range	Description
zeus_denominator	int	3	2 ~ 6	Sparsity denominator
zeus_modular	string	"0,1"	-	Comma-separated list of remainders to skip
zeus_acc_start	int	10	0 ~ 100	Acceleration window start step
zeus_acc_end	int	45	-100 ~ 200	Acceleration window end step
zeus_interp_mode	enum	psi	psi, x_0	Interpolation mode
zeus_caching_mode	enum	reuse_interp	reuse_interp, interp_all, reuse_all	Caching strategy
zeus_max_interval	int	4	1 ~ 20	Maximum consecutive skipped steps
zeus_lagrange_term	int	3	0 ~ 5	Lagrange interpolation order (0 = disabled)
zeus_lagrange_int	int	6	1 ~ 20	Lagrange anchor sampling interval
zeus_lagrange_step	int	24	5 ~ 100	Step at which Lagrange interpolation activates

Default values are from the official flux_demo.py.

Parameter Details

zeus_denominator (Sparsity Denominator)

Controls the skip period. Every denominator steps form a group; within each group, modular determines which steps are skipped.

• Larger values → more steps per group → wider range of possible skip ratios
• Typically set to 3 (combined with modular="0,1" for a 2/3 skip rate)

zeus_modular (Skip Remainder List)

Comma-separated list of integers. A step is skipped when step_index % denominator matches any value in this list.

• denominator=3, modular="0,1" → skip 2 out of every 3 steps, compute only 1/3 → ~3x speedup
• denominator=2, modular="0" → skip 1 out of every 2 steps, compute 1/2 → ~2x speedup
• denominator=3, modular="1" → skip 1 out of every 3 steps, compute 2/3 → ~1.5x speedup
• denominator=4, modular="0,1,2" → skip 3 out of every 4 steps → ~4x speedup (aggressive)

Note: Each value in modular must be < denominator.

zeus_acc_start / zeus_acc_end (Acceleration Window)

Only steps within the [acc_start, acc_end) range are eligible for skipping. Steps outside this window are always fully computed.

• The first few steps (typically 3~10) must be fully computed to establish the initial trajectory
• The last few steps must be fully computed to ensure final output quality
• Internally, acc_start is clamped to max(acc_start, 3) (the algorithm depends on prior data)
• For 50-step sampling, a typical range is (8~10, 45~47)

zeus_interp_mode (Interpolation Mode)

Determines how model outputs are reconstructed for skipped steps:

• psi (PSI linear extrapolation): Linear extrapolation in model output space (epsilon_{t-1} = epsilon_t + (epsilon_t - epsilon_{t+1})). Fast and suitable for most scenarios. Recommended as default.
• x_0 (trajectory interpolation): Uses Simpson's rule in the denoising trajectory space. May be more accurate for complex generation scenarios, but slightly slower.

zeus_caching_mode (Caching Strategy)

Controls how cached interpolation results are reused during consecutive skipped steps:

• reuse_interp (recommended): Alternates between new interpolation and cached interpolation during consecutive skips. Best balance between speed and quality.
  • Odd consecutive skips: reuse the previously cached interpolation
  • Even consecutive skips: compute a new interpolation
• interp_all: Recompute interpolation for every skipped step. Highest quality but more computation.
• reuse_all: Always reuse the previously cached output. Fastest but lowest quality.

zeus_max_interval (Maximum Consecutive Skips)

Safety valve — after this many consecutive skipped steps, a full computation is forced.

• Prevents error accumulation from too many consecutive skips
• Typical values: 4 (FLUX/SDXL) or 6 (video models/SD)
• Lower values are more conservative (better quality but reduced speedup)

zeus_lagrange_term (Lagrange Interpolation Order)

Enables Lagrange polynomial interpolation for higher-precision reconstruction in later steps:

• 0: Disable Lagrange interpolation; use only PSI/x_0
• 3: 3rd-order Lagrange polynomial (recommended for FLUX, CogVideo)
• 4: 4th-order Lagrange polynomial (recommended for SD, SDXL, Wan2.1)

When lagrange_term > 0, the algorithm uses PSI/x_0 interpolation in [acc_start, lagrange_step) and switches to Lagrange interpolation in [lagrange_step, acc_end).

zeus_lagrange_int (Lagrange Anchor Interval)

How many steps apart each Lagrange anchor point is recorded (used for polynomial fitting).

• Smaller values → denser anchors → more precise fitting but increased overhead
• Typical values: 6 (FLUX, CogVideo) or 4 (SD, SDXL, Wan2.1)
• Requirement: lagrange_step % lagrange_int == 0

zeus_lagrange_step (Lagrange Activation Step)

The step at which Lagrange interpolation replaces PSI/x_0.

• Before this step: PSI/x_0 interpolation is used
• After this step: Lagrange polynomial interpolation is used
• Typical value: 24 (for 50-step sampling)
• Requirement: lagrange_step % lagrange_int == 0

Official Recommended Configurations

The following parameters are from the ZEUS official repository demo files, based on 50-step sampling:

Image Models

Model	Demo File	denominator	modular	acc_start	acc_end	interp_mode	caching_mode	max_interval	lagrange_term	lagrange_int	lagrange_step
FLUX	flux_demo.py	3	(0,1)	10	45	psi	reuse_interp	4	3	6	24
SD 2.1	sd_demo.py	3	(0,1)	10	45	psi	reuse_interp	6	4	4	24
SDXL	xl_demo.py	3	(0,1)	10	45	psi	reuse_interp	4	4	4	24

Video Models

Model	Demo File	denominator	modular	acc_start	acc_end	interp_mode	caching_mode	max_interval	lagrange_term	lagrange_int	lagrange_step
Wan2.1	wan2_demo.py	3	(0,1)	8	47	psi	-	6	4	4	24
CogVideoX	cogvideo_demo.py	3	(0,1)	8	47	psi	-	6	3	6	24

Key Takeaways

1. All models use denominator=3, modular=(0,1) as the universal configuration (2/3 skip rate, ~3x speedup)
2. Image models typically use acc_range=(10, 45), while video models use a wider window acc_range=(8, 47)
3. Video models set max_interval to 6 (more permissive), while image models use 4
4. SD/SDXL/Wan2.1 prefer lagrange_term=4, lagrange_int=4 (higher order, denser anchors)
5. FLUX/CogVideo prefer lagrange_term=3, lagrange_int=6 (slightly lower order, sparser anchors)
6. All models use lagrange_step=24 consistently

Supported Samplers

euler, heun, heunpp2, dpm_2, lms, dpm_fast, dpm_adaptive, dpmpp_2m, ipndm, ipndm_v, deis, res_multistep, gradient_estimation, ddim, euler_ancestral, dpm_2_ancestral

Reference

• Paper: ZEUS: Zero-shot Efficient Unified Sparsity for Diffusion Models
• GitHub: https://github.com/Ting-Justin-Jiang/ZEUS

Citation

@misc{zeus2025,
  title        = {ZEUS: Zero-shot Efficient Unified Sparsity for Generative Models},
  author       = {Yixiao Wang and Ting Jiang and Zishan Shao and Hancheng Ye and Jingwei Sun and Mingyuan Ma and Jianyi Zhang and Yiran Chen and Hai Li},
  year         = {2025},
  howpublished = {https://yixiao-wang-stats.github.io/zeus/},
  note         = {Code and project page available at {https://github.com/Ting-Justin-Jiang/ZEUS}}
}