[Paper] InSPECT: Invariant Spectral Features Preservation of Diffusion Models

Source: arXiv - 2512.17873v1

Overview

Diffusion models have become the go‑to technique for high‑quality image synthesis, but their classic formulation—gradually corrupting an image all the way to pure Gaussian noise and then learning to reverse that process—poses a heavy computational burden. InSPECT (Invariant Spectral Feature‑Preserving Diffusion Model) tackles this head‑on by keeping certain spectral (Fourier‑domain) characteristics of the data intact throughout both the forward “noising” and backward “denoising” steps. The result is a model that converges faster, generates more diverse samples, and does so with noticeably lower compute cost.

Key Contributions

• Invariant spectral preservation: Introduces a principled way to maintain selected Fourier coefficients during diffusion, ensuring that essential image structure survives the noise‑adding phase.
• Smooth convergence to random noise: Designs a forward schedule where the retained spectral components gradually blend into a predefined random noise spectrum, preserving diversity while keeping a stable feature backbone.
• Efficiency boost: Demonstrates up to 39 % lower FID and 46 % higher IS compared with the vanilla DDPM after only 10 K training steps, translating to fewer training epochs for comparable quality.
• Broad empirical validation: Experiments on CIFAR‑10, CelebA, and LSUN show consistent gains across low‑resolution and higher‑resolution datasets.
• First systematic analysis: Provides the inaugural theoretical and empirical study of invariant spectral features in diffusion models, opening a new research direction.

Methodology

1. Spectral decomposition: Each image is transformed into the Fourier domain. A subset of low‑frequency coefficients—those that capture global shape and color layout—are marked as invariant.
2. Forward diffusion with constraints: Instead of adding isotropic Gaussian noise to every pixel, the algorithm injects noise only into the mutable (high‑frequency) components while slowly nudging the invariant coefficients toward a target random spectrum. This creates a smooth trajectory from the original image to a controlled noise state.
3. Backward denoising network: The neural network (a UNet‑style architecture, as in standard DMs) receives both the noisy image and a spectral hint that encodes the current invariant coefficients. The loss is computed only on the mutable part, allowing the network to focus on reconstructing fine details while the invariant backbone guides global consistency.
4. Training schedule: The authors adopt a cosine‑based noise schedule for the mutable spectrum and a linear interpolation for the invariant part, ensuring that the two processes stay synchronized.
5. Sampling: At generation time, the model starts from the prescribed random noise spectrum, progressively restores the invariant coefficients, and finally refines the high‑frequency details via the learned denoiser.

The overall pipeline can be visualized as a dual‑track diffusion: one track (low‑freq) follows a deterministic, feature‑preserving path; the other (high‑freq) behaves like a classic diffusion process.

Results & Findings

• Faster convergence: InSPECT reaches a comparable FID to a fully trained DDPM after roughly half the number of training steps.
• Higher diversity: The Inception Score improvements indicate that preserving global spectral cues helps avoid mode collapse, especially on datasets with varied poses and backgrounds.
• Smoother training dynamics: Loss curves exhibit lower variance, suggesting that the invariant backbone stabilizes the optimization landscape.

Qualitative samples show sharper edges and more coherent global structures (e.g., facial symmetry in CelebA) while still exhibiting the stochastic variety expected from diffusion models.

Practical Implications

• Reduced training cost: Teams can achieve state‑of‑the‑art image synthesis with fewer GPU hours, making diffusion models more accessible for startups and research labs with limited resources.
• Better control over global attributes: Because the invariant spectrum encodes coarse layout, developers can manipulate these coefficients to steer generation (e.g., enforce a particular pose or color palette) without retraining the whole model.
• Potential for downstream tasks: The preserved spectral features can be reused for tasks like image editing, super‑resolution, or conditional generation where maintaining global consistency is crucial.
• Compatibility with existing pipelines: InSPECT’s UNet backbone and training schedule are drop‑in replacements for standard DDPM codebases, easing adoption in frameworks such as PyTorch‑Lightning or Hugging Face Diffusers.

Overall, the paper suggests a practical recipe for speed‑up‑and‑quality‑boost that can be integrated into production‑grade generative pipelines, from content creation tools to data augmentation services.

Limitations & Future Work

• Spectral selection heuristic: The current method fixes a low‑frequency cutoff; adaptive or learned selection of invariant components could further improve results.
• Scalability to ultra‑high resolutions: Experiments stop at 256 × 256; extending the approach to 1024 × 1024 images may require more sophisticated frequency partitioning.
• Conditional generation: While the paper focuses on unconditional synthesis, integrating class or text conditioning with invariant spectra remains an open question.
• Theoretical guarantees: The authors provide empirical evidence but a formal analysis of why preserving certain Fourier modes aids convergence is still pending.

Future research directions include learning the invariant subspace jointly with the diffusion network, exploring multi‑scale spectral preservation, and applying the concept to other modalities such as audio or 3‑D point clouds.

Authors

• Baohua Yan
• Qingyuan Liu
• Jennifer Kava
• Xuan Di

Paper Information

• arXiv ID: 2512.17873v1
• Categories: cs.CV
• Published: December 19, 2025
• PDF: Download PDF