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ResilPhase: Plug-and-Play Phase Mapping and Noise-Resilient Macro-Trajectory Extrapolation for Diffusion Acceleration

ResilPhase is a plug-and-play framework that accelerates diffusion models by reformulating inference as stable macro-trajectory extrapolation in ODE space, utilizing a derivative-free barycentric Lagrange extrapolator and bounded phase mapping to overcome the quality degradation and instability inherent in existing cache-then-forecast methods.

Original authors: Qicheng Zhao, Yu Li, Qi Sun, Zheyu Yan

Published 2026-06-26

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CC BY 4.0

Original authors: Qicheng Zhao, Yu Li, Qi Sun, Zheyu Yan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict the path of a rollercoaster. To do this accurately, you usually need to check the car's position at every single second, calculate how fast it's going, how fast that speed is changing (acceleration), and how that is changing (jerk).

The Problem: The "Over-Complicated" Rollercoaster
Current AI image and video generators (called Diffusion Models) work like this rollercoaster. To create a picture, they take hundreds of tiny steps, checking the image's state at every single moment. This is incredibly slow.

To speed things up, recent methods tried to be clever: "Let's skip the middle steps! We'll just look at the last few points and guess where the car will be next." They used math formulas (polynomials) to draw a line through these points.

However, the paper argues these methods are failing because they are looking at the wrong things:

They are looking at the wrong details: Instead of looking at the whole rollercoaster track, they are trying to predict the tiny, jittery movements of individual bolts on the car. These tiny movements are chaotic and noisy. If you guess wrong on one bolt, the error multiplies as you move up the car, ruining the whole prediction.
They are using the wrong math: They try to calculate "speed" and "acceleration" by looking at the difference between noisy points. It's like trying to measure the wind speed by looking at a single, shaking leaf. The math amplifies the noise, causing the prediction to go wildly off-track.
The "Edge Effect": When you try to guess the future based on a straight line of points, the further out you guess, the more the line tends to wiggle and explode at the edges. This is a known math problem called "Runge's phenomenon."

The Solution: ResilPhase
The authors created a new system called ResilPhase (Resilient Phase Mapping) to fix these three problems. Here is how it works, using simple analogies:

1. The "Big Picture" Strategy (Global Drift)

Instead of trying to predict the jittery movement of every single bolt (layer-by-layer features), ResilPhase asks a simpler question: "If we start here and end there, what is the total distance traveled?"

They call this the Global Drift. Imagine you don't care about the bumps in the road; you only care about the straight line from the station to the finish line. By predicting this big, smooth movement, the AI avoids the "domino effect" where small errors pile up and destroy the image. It skips the messy middle details and focuses on the end-to-end journey.

2. The "No-Speedometer" Strategy (Derivative-Free)

Old methods tried to calculate speed and acceleration to guess the future. But because the data is noisy, calculating speed made the noise explode.

ResilPhase says, "Don't calculate speed. Just look at the dots."
They use a special math trick called Barycentric Lagrange Interpolation. Think of this as drawing a smooth curve through a set of dots without ever trying to measure how fast the pen was moving between them. It ignores the noisy "speed" data entirely and just connects the dots in the most stable way possible. This stops the noise from ruining the prediction.

3. The "Magic Map" Strategy (Phase Mapping)

Even with the right strategy, guessing the future based on evenly spaced points (like checking the clock every 1 second) causes those wild wiggles at the edges (Runge's phenomenon).

ResilPhase introduces Phase Mapping. Imagine you have a rubber map of time.

The Old Way: You stretch the map evenly. The edges get stretched too thin and tear (errors explode).
The New Way: You use a special "elastic" map (called Chebyshev or Balanced Mapping). You stretch the middle of the map more and squeeze the edges. This rearranges the points so that the math stays stable, even when you are guessing far into the future. It keeps the prediction tight and accurate, preventing the "wiggles" from destroying the image.

The Result

By combining these three ideas—looking at the big picture instead of the noise, ignoring speed calculations, and stretching the time map to keep things stable—ResilPhase can generate images and videos 5 times faster than before.

Crucially, it doesn't just get faster; it actually gets better. While other fast methods produce blurry, distorted, or weird images when they try to go too fast, ResilPhase keeps the details sharp and the colors correct, even at extreme speeds.

In short: ResilPhase stops the AI from getting confused by tiny, noisy details and chaotic math, allowing it to see the "big picture" and generate high-quality art in a fraction of the time.

Technical Summary: ResilPhase

Problem Statement

Diffusion Transformers (DiTs) have established themselves as the gold standard for high-fidelity visual generation due to their scalable architecture. However, their reliance on iterative denoising processes creates a significant inference latency bottleneck, often requiring tens to hundreds of sequential forward steps that cannot be parallelized. Recent training-free acceleration efforts have shifted from passive "cache-then-reuse" paradigms to "cache-then-forecast" schemes, which use polynomials to predict feature trajectories.

Despite these advancements, existing methods suffer from severe quality degradation at high acceleration ratios. The authors identify three root causes for this failure:

Spatial Instability: Most methods rely on layer-wise forecasting, fitting polynomials to highly erratic micro-features within Transformer blocks. This causes prediction errors to cascade exponentially across network depth and incurs massive memory overhead.
Temporal Instability (Derivative Fallacy): Current forecasting methods rely on derivative-based approximations (e.g., Taylor series, Hermite polynomials). While the macro-trajectory of the diffusion process is smooth, its higher-order temporal derivatives are intrinsically chaotic. Estimating these via finite differences exponentially amplifies noise, leading to divergent predictions.
Numerical Instability (Runge's Phenomenon): Performing polynomial extrapolation over uniform, discrete time steps triggers Runge's phenomenon, causing uncontrollable edge oscillations and catastrophic quality degradation at aggressive acceleration ratios.

Methodology: ResilPhase

The authors propose ResilPhase, a noise-resilient, plug-and-play acceleration framework that reformulates accelerated inference as stable macro-trajectory extrapolation in Ordinary Differential Equation (ODE) space. The framework addresses the identified bottlenecks through three core components:

1. ODE-Aligned Macro-Trajectory Targeting (Global Drift)

Instead of predicting intermediate layer-wise features, ResilPhase shifts the prediction target to the Global Drift (GD). The GD is defined as the end-to-end state displacement between the model's initial input and its final output ( $D(x_t) = G(x_t) - x_t$ ).

Mechanism: A single macro-predictor forecasts the GD for skipped steps, and the final output is reconstructed by adding this drift to the input.
Benefit: This approach aligns the extrapolator with the continuous probability flow ODE, strictly severing the spatial cascading error accumulation inherent in layer-wise methods. It reduces the error bound from being dependent on network depth ( $O((1+L_f)^L)$ ) to a constant ( $O(1)$ ) and eliminates the memory overhead of caching block features.

2. Derivative-Free Barycentric Lagrange Extrapolator

To bypass the "derivative fallacy" where higher-order derivatives are noisy, ResilPhase employs a purely derivative-free approach.

Mechanism: The framework utilizes Barycentric Lagrange Interpolation. Unlike standard Lagrange interpolation which has $O(m^2)$ complexity, the barycentric form allows weights to be precomputed and cached, reducing complexity to $O(m)$ .
Benefit: By avoiding finite-difference approximations of derivatives, the method completely bypasses the amplification of gradient noise and chaotic high-order derivatives, resulting in significantly lower and more stable prediction errors across varying extrapolation intervals.

3. Plug-and-Play Phase Mapping

To suppress the numerical instability caused by Runge's phenomenon on uniform time steps, the authors introduce a Phase Mapping mechanism.

Mechanism: This technique non-linearly projects discrete time steps ( $t$ $t$ ) into a bounded phase domain ( $s$ $s$ ). Two specific mappings are proposed:
- Chebyshev Mapping: Uses Chebyshev nodes to project time steps, optimal for class-conditional generation.
- Balanced Mapping: A data-driven, adaptive strategy using a hyperbolic tangent function to dynamically confine mapped coordinates based on the spread of recent timesteps. This is tailored for complex text-to-image and text-to-video tasks.
Benefit: By remapping the extrapolation domain, the method minimizes the node-dependent error term in the Lagrange interpolation error bound, effectively transforming a divergent numerical issue into a stable prediction.

Key Contributions

Global Drift Targeting: A shift from layer-wise feature prediction to end-to-end Global Drift forecasting, which eliminates spatial cascading errors and memory overhead while aligning with the continuous ODE.
Derivative-Free Extrapolation: The introduction of a noise-resilient, $O(N)$ Barycentric Lagrange extrapolator that bypasses the inherent noise and chaotic derivatives of finite-difference approximations.
Phase Mapping Mechanism: A theoretically grounded, plug-and-play technique that regularizes the extrapolation domain via Chebyshev or Balanced Mapping, strictly minimizing the polynomial extrapolation error bound and suppressing oscillatory growth.
Plug-and-Play Stabilizer: The demonstration that Phase Mapping can be integrated into existing derivative-based accelerators (e.g., TaylorSeer, HiCache) to improve their stability and performance.

Experimental Results

The authors evaluated ResilPhase on FLUX.1-dev (text-to-image), HunyuanVideo (text-to-video), and DiT-XL/2 (class-conditional ImageNet generation).

Text-to-Image (FLUX.1-dev): ResilPhase achieved approximately 4.97× speedup while maintaining an ImageReward of 1.0258, outperforming the leading baseline TaylorSeer (0.6241) by over 60%. It also demonstrated a 52% lower LPIPS score compared to TaylorSeer. Qualitative results showed ResilPhase preserved detailed structures and color accuracy where baselines suffered from severe artifacts.
Text-to-Video (HunyuanVideo): At a ~5× speedup, ResilPhase achieved a VBench score of 79.78 and a 10% lower LPIPS compared to the SOTA TeaCache. It maintained temporal coherence and semantic accuracy, whereas competitors exhibited object blur and motion distortion.
Class-Conditional Generation (ImageNet): On DiT-XL/2, ResilPhase achieved a 2.78× speedup with an FID of 2.347, outperforming the full 50-step DDIM baseline (FID 2.367). At a more aggressive 4.41× speedup, it maintained an FID of 2.832, significantly outperforming competitors like SpeCa (FID 6.866) and ClusCa (FID 3.251).
Ablation Studies: Experiments confirmed that Global Drift targeting outperforms layer-wise prediction and that Balanced Mapping is superior to Chebyshev Mapping for text-conditioned tasks. Integrating Phase Mapping into existing accelerators consistently improved their ImageReward and reduced extrapolation error bounds.

Significance and Claims

The paper claims that ResilPhase establishes a new state-of-the-art balance between inference acceleration and exceptional generation quality. By addressing the spatial, temporal, and numerical limitations of existing paradigms, it enables aggressive acceleration ratios (up to ~5×) without the severe quality degradation previously observed.

The authors position ResilPhase not only as a standalone high-performance accelerator but also as a robust, plug-and-play stabilizer that can mitigate extrapolation errors in existing derivative-based accelerators. The work provides a theoretical and practical framework for stable macro-trajectory extrapolation, offering a viable path toward real-time and large-scale deployment of Diffusion Transformers.