Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise

• URL: http://arxiv.org/abs/2510.09660v3
• Date: Wed, 22 Oct 2025 00:45:29 GMT
• Title: Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise
• Authors: Luca Scimeca, Thomas Jiralerspong, Berton Earnshaw, Jason Hartford, Yoshua Bengio,
• Abstract summary: Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit.<n>In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model.<n>We introduce an anisotropic noise operator that shapes these biases by replacing the isotropic forward covariance with a structured, frequency-diagonal covariance.
• Score: 43.07594740645669
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion Probabilistic Models (DPMs) have achieved strong generative performance, yet their inductive biases remain largely implicit. In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model. We introduce an anisotropic noise operator that shapes these biases by replacing the isotropic forward covariance with a structured, frequency-diagonal covariance. This operator unifies band-pass masks and power-law weightings, allowing us to emphasize or suppress designated frequency bands, while keeping the forward process Gaussian. We refer to this as spectrally anisotropic Gaussian diffusion (SAGD). In this work, we derive the score relation for anisotropic covariances and show that, under full support, the learned score converges to the true data score as $t\!\to\!0$, while anisotropy reshapes the probability-flow path from noise to data. Empirically, we show the induced anisotropy outperforms standard diffusion across several vision datasets, and enables selective omission: learning while ignoring known corruptions confined to specific bands. Together, these results demonstrate that carefully designed anisotropic forward noise provides a simple, yet principled, handle to tailor inductive bias in DPMs.

Related papers

• Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold [19.059115911590776]
  We explicitly characterize what diffusion model generates, by proposing a log-density ridge manifold.<n>We show how the generated data relate to this manifold as inference dynamics progresses.<n>More detailed understanding of training dynamics will lead to more accurate quantification of the generation inductive bias.
  arXiv  Detail & Related papers  (2026-02-05T18:55:03Z)
• Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Study [3.265950484493743]
  Diffusion models can be prone to memorization.<n>Regularization on the score has the same effect as increasing the size of the training dataset.<n>This perspective highlights two regularization mechanisms taking place in denoising diffusions.
  arXiv  Detail & Related papers  (2025-05-28T20:22:18Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Shaping Inductive Bias in Diffusion Models through Frequency-Based Noise Control [43.87692887705523]
  We build inductive biases into the training and sampling of Diffusion Probabilistic Models (DPMs)<n>We show that different datasets necessitate different inductive biases, and that appropriate frequency-based noise control induces increased generative performance compared to standard diffusion.
  arXiv  Detail & Related papers  (2025-02-14T15:46:37Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• On the Relation Between Linear Diffusion and Power Iteration [42.158089783398616]
  We study the generation process as a correlation machine'' We show that low frequencies emerge earlier in the generation process, where the denoising basis vectors are more aligned to the true data with a rate depending on their eigenvalues. This model allows us to show that the linear diffusion model converges in mean to the leading eigenvector of the underlying data, similarly to the prevalent power iteration method.
  arXiv  Detail & Related papers  (2024-10-16T07:33:12Z)
• Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models [59.331993845831946]
  Diffusion models benefit from instillation of task-specific information into the score function to steer the sample generation towards desired properties. This paper provides the first theoretical study towards understanding the influence of guidance on diffusion models in the context of Gaussian mixture models.
  arXiv  Detail & Related papers  (2024-03-03T23:15:48Z)
• Score-based Continuous-time Discrete Diffusion Models [102.65769839899315]
  We extend diffusion models to discrete variables by introducing a Markov jump process where the reverse process denoises via a continuous-time Markov chain. We show that an unbiased estimator can be obtained via simple matching the conditional marginal distributions. We demonstrate the effectiveness of the proposed method on a set of synthetic and real-world music and image benchmarks.
  arXiv  Detail & Related papers  (2022-11-30T05:33:29Z)
• Diffusion-GAN: Training GANs with Diffusion [135.24433011977874]
  Generative adversarial networks (GANs) are challenging to train stably. We propose Diffusion-GAN, a novel GAN framework that leverages a forward diffusion chain to generate instance noise. We show that Diffusion-GAN can produce more realistic images with higher stability and data efficiency than state-of-the-art GANs.
  arXiv  Detail & Related papers  (2022-06-05T20:45:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.