Diffusion models like Midjourney, Stable Diffusion, and Sora have transformed how we create digital art, videos, and realistic images from simple text prompts. They power a new generation of creative tools—but they share one major limitation: speed. Generating a single high-resolution image with a model like SDXL can take tens of seconds, making real-time or interactive applications cumbersome.

Why are they so slow? It all comes down to their core mechanism. Diffusion models start from pure noise (think of TV static) and gradually refine this noise into a coherent image through dozens or even hundreds of steps. At each step, a large neural network—called the noise predictor—estimates how much noise remains to be removed. Running this heavy network repeatedly dominates the computation time.

Yet, not all these steps are equally important. Some may only make minor adjustments that don’t significantly affect the final image. A new research paper, “Training-Free Adaptive Diffusion with Bounded Difference Approximation Strategy”, introduces AdaptiveDiffusion, a clever, training-free method that identifies and skips redundant noise prediction steps. The result is a speedup of up to 5×—with virtually no loss in image quality.

The authors achieve this by introducing an adaptive criterion: an intelligent mechanism that decides which steps are worth computing based on the complexity of the prompt and the stability of the generation process. Let’s unpack how it works.

Understanding Why Diffusion Is Slow

Diffusion generation follows the reverse denoising process. The model begins with random noise \(x_T\) and iteratively denoises it through \(T\) timesteps until obtaining the clean output \(x_0\).

At each step \(i\):

  • The network predicts noise using \(\epsilon_\theta(x_i, t_i, c)\), where \(c\) is a conditioning input (like a text prompt or image embedding).
  • The scheduler uses this prediction to update the latent image:
\[ x_{i-1} = f(i-1) \cdot x_i - g(i-1) \cdot \epsilon_\theta(x_i, t_i) \]

Here, \(f\) and \(g\) are coefficients determined by the sampling strategy (DDIM, DPM-Solver++, Euler, etc.).

Executing this noise prediction \(T\) times dominates inference cost. In models like SDXL, each of the 50 steps involves a full pass through a large U-Net—making image generation expensive.

Acceleration methods traditionally fall into three categories:

  1. Reducing sampling steps (e.g., DDIM, DPM-Solver): fewer total timesteps, trading speed for quality.
  2. Optimizing model architecture (e.g., DeepCache): caching intermediate computations within the U-Net.
  3. Parallel inference: running multiple steps concurrently.

However, all these approaches use a fixed acceleration schedule—the same number of steps for every prompt. AdaptiveDiffusion’s authors noticed that prompts differ dramatically in complexity. A simple scene (“a red ball on a white background”) requires fewer updates than a vivid movie-like prompt (“an 18th-century market painted in oil style”). Why force both to take the same number of steps?

Different prompts require different denoising paths to generate a high-quality image. For a simple prompt, only 20 out of 50 steps might be needed, while a more complex one requires 26 steps to achieve the same quality.

Figure 1: Different prompts need different numbers of noise predictions for near-lossless generation. Using a fixed step count wastes computation.

This observation inspires a new paradigm—prompt-adaptive acceleration, where the denoising step count adjusts dynamically to the prompt.

How AdaptiveDiffusion Skips Work Intelligently

At its core, AdaptiveDiffusion introduces a mechanism to decide—at each denoising step—whether the model should perform a full noise prediction or simply reuse the last one.

A high-level overview of AdaptiveDiffusion. In a standard process, the noise prediction model runs at every step. With AdaptiveDiffusion, a “Third-order Estimator” decides whether to run the model or reuse a cached noise prediction, skipping the heavy computation.

Figure 2: AdaptiveDiffusion integrates an estimator that selectively triggers or skips noise prediction, reusing cached results where the process is stable.

What Does “Skipping” Mean?

Skipping doesn’t mean skipping the entire update step—only the expensive noise prediction. The latent updates themselves (the multiplications by \(f\) and \(g\)) are fast and essential for refining the output.

When a step \(i\) is skipped, AdaptiveDiffusion reuses the noise predicted at the previous step:

\[ \begin{aligned} x_i &= f(i) \cdot x_{i+1} - g(i) \cdot \epsilon_\theta(x_{i+1}, t_{i+1}) \\ x_{i-1} &= f(i-1) \cdot x_i - g(i-1) \cdot \epsilon_\theta(x_{i+1}, t_{i+1}) \end{aligned} \]

This saves a forward pass through the U-Net—reducing latency while maintaining image fidelity.

A comparison of different skipping strategies. (a) Full 50-step generation. (b) AdaptiveDiffusion skips 25 noise predictions but performs all 50 latent updates, resulting in a good image. (c) A standard 25-step generation. (d) Skipping both noise prediction and latent updates for 25 steps results in pure noise.

Figure 3: Skipping only the noise prediction (b) preserves quality, while skipping both prediction and latent updates (d) fails completely.

The challenge? Knowing when it’s safe to skip.

Measuring Stability: A “Jerk” Detector for Diffusion

To decide when to skip, AdaptiveDiffusion measures how stable the denoising process is—using derivatives of the latent states across timesteps.

The authors introduce higher-order latent differences:

  • 1st-order difference — Change between consecutive steps:
    \(\Delta x_i = x_i - x_{i+1}\)
  • 2nd-order difference — Change rate of that change:
    \(\Delta^{(2)} x_i = \Delta x_i - \Delta x_{i+1}\)
  • 3rd-order difference — Change of acceleration, analogous to “jerk”:
    \(\Delta^{(3)} x_i = \Delta^{(2)} x_i - \Delta^{(2)} x_{i+1}\)

By analyzing these signals throughout full denoising runs, the authors discovered an intriguing pattern: the 3rd-order latent difference strongly correlates with skip-worthy steps.

A comparison of different order latent differences against the optimal skipping path. The 1st and 2nd order differences are noisy, but the relative 3rd-order difference shows a clear correlation with when steps should be skipped.

Figure 4: The 3rd-order latent difference captures when new noise predictions matter. Low values correspond to stable regions where skipping is safe.

When the “jerk” is small, the latent trajectory is smooth—indicating redundancy. When it spikes, new noise predictions are necessary to capture rapid transitions.

The Third-Order Estimation Criterion

This insight leads to a simple rule to decide at each step:

\[ \xi(x_{i-1}) = \left\| \Delta^{(3)} x_{i-1} \right\| \ge \delta \| \Delta x_i \| \]

Here:

  • \(\Delta^{(3)} x_{i-1}\) is the third-order latent difference (jerk).
  • \(\Delta x_i\) is the first-order difference (velocity).
  • \(\delta\) is a small threshold hyperparameter.

Interpretation:
If the jerk magnitude exceeds a certain scaled threshold, compute a new noise prediction. If not, reuse the previous one.

To prevent accumulated error from too many consecutive skips, the authors add another parameter—\(C_{\text{max}}\)—the maximum allowed number of consecutive skipped steps.

Validation of the third-order estimator. (a) The path predicted by the estimator closely matches the optimal path found by greedy search. (b) Error accumulates over long skips, controlled by \\(C_{max}\\). (c) Statistical tests confirm strong correlation between estimated and optimal paths.

Figure 5: The third-order estimator strongly correlates with optimal skipping behavior, providing a statistically valid foundation for adaptive acceleration.

This criterion is training-free (no gradient updates or finetuning) and compatible with any diffusion model. It simply reads the latent states during inference and decides whether to skip based on a mathematical signal.

Results: Does AdaptiveDiffusion Really Work?

The authors evaluated AdaptiveDiffusion across multiple tasks—text-to-image, image-to-video, and text-to-video—using popular models like SD-1.5, SDXL, I2VGen-XL, and ModelScopeT2V.

Image Generation

On the MS-COCO benchmark, AdaptiveDiffusion consistently achieved faster inference and better image quality.

Quantitative results for text-to-image generation on the MS-COCO dataset. AdaptiveDiffusion (“Ours”) achieves higher quality scores (higher PSNR, lower LPIPS and FID) and often better speedups than baselines across various models and schedulers.

Table 1: Across schedulers and models, AdaptiveDiffusion (“Ours”) surpasses DeepCache and Adaptive DPM-Solver in both speed and fidelity.

For SDXL with Euler sampling, AdaptiveDiffusion achieved a 2.01× speedup while maintaining near-original quality (LPIPS ≈ 0.168, PSNR ≈ 24.3).

Visual comparisons underline the superiority of AdaptiveDiffusion’s results.

Qualitative comparison of text-to-image generation. The images generated by AdaptiveDiffusion (“Ours”) are visually much closer to the “Original” than those from DeepCache, especially in preserving fine details and textures.

Figure 6: Side-by-side comparison shows AdaptiveDiffusion’s output mirrors the original full-step image, outperforming DeepCache.

Video Generation

Video generation adds temporal complexity. The method must not only preserve per-frame quality but also keep frames coherent over time.

Quantitative results for video generation. AdaptiveDiffusion shows a massive quality improvement over DeepCache, especially in per-frame metrics like PSNR and LPIPS, while also better preserving temporal consistency.

Table 3: AdaptiveDiffusion greatly improves both spatial fidelity and temporal consistency on challenging video benchmarks.

AdaptiveDiffusion achieved substantial gains in PSNR (up to +6.4 dB) and LPIPS, with low Fréchet Video Distance (FVD), meaning smoother motion across frames.

Qualitative comparison for image-to-video generation. AdaptiveDiffusion maintains high frame quality and consistency, closely matching the original generation.

Figure 7 & 8: Visual comparisons confirm lossless temporal coherence. Most prompts on MS-COCO require only ~26 noise prediction steps, proving significant redundant computation can be skipped.

Broader Implications

AdaptiveDiffusion demonstrates how mathematical insight—in this case, a third-order differential criterion—can achieve major efficiency gains without sacrificing quality.

Key takeaways:

  1. Adaptivity Matters: Prompts differ in complexity. A flexible system that allocates computation accordingly outperforms any fixed budget strategy.
  2. The Power of the “Jerk”: The third-order latent difference is a surprisingly precise indicator of when the generation process truly needs recomputation.
  3. Training-Free Universality: AdaptiveDiffusion doesn’t require retraining or architectural modification—just a smart inference-side heuristic. It works across models and tasks.

By dynamically skipping redundant noise predictions, AdaptiveDiffusion cuts latency by up to five times, enabling near real-time image and video generation. This method not only pushes diffusion efficiency forward but also opens the door to interactive creativity tools, where responsive generative models can keep up with human imagination.