Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
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A fourier space perspective on diffusion models
14 Pith papers cite this work, alongside 2 external citations. Polarity classification is still indexing.
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abstract
Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks.
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Low-Pass Flow Matching modifies Flow Matching via an operator-modulated interpolant inducing time-varying spectral bias from source spectrum to frequency-decaying bias, improving or preserving quality while reducing sampling cost on unconditional image generation including Galaxy10.
SKILD unifies unconditional image generation and continuous super-resolution in one diffusion model via scale-invariant k-space dynamics where the reverse process handles both tasks by varying only the starting timestep.
HDP3 is a pocket-scale 3D diffusion policy with a Diffusion Mixer decoder that achieves state-of-the-art visuomotor control using two-step DDIM inference and under 1% of the parameters of prior 3D diffusion policies.
CSFlow derives inference-time timestep weights for flow matching by matching per-step frequency content to human CSF, yielding 4.7% FID reduction and smaller gains on IS and GenEval.
CNS is a plug-and-play stochastic sampler for diffusion models that uses timestep- and frequency-dependent colored noise to allocate energy to unresolved bands, producing lower FID scores than standard ODE/SDE baselines on ImageNet-256.
FGO guides diffusion policy generation via expanding spectral bands on sub-frequency manifolds to improve action smoothness on 15 robotic manipulation tasks.
SpectralDiT adds timestep-conditioned spectral residual correction to flow-matching DiTs and reports FID reductions of 5% on CIFAR-10 and 8.7% relative on ImageNet-100 latent diffusion with under 2% added parameters.
HyFAD combines sequential time-to-frequency diffusion with frequency-aware step embeddings to achieve claimed state-of-the-art time series imputation on benchmarks.
Flicker-DDPM accelerates DDPM sampling by injecting 1/f colored noise matched to image spectra, achieving similar quality with 3.33 times fewer steps on CIFAR-10.
DSFM generates synthetic fMRI time series via DWT-DCT dual transforms and spectral flow matching to improve downstream brain network classification.
Spectral Progressive Diffusion progressively grows resolution during denoising of pretrained diffusion models via spectral noise expansion and a power-spectrum-derived schedule, enabling training-free speedups and a fine-tuning recipe.
FREE-Switch dynamically switches LoRA adapters using frequency importance per diffusion step and adds semantic alignment to reduce content drift when merging specialized image generators.
FRAMER improves real-world super-resolution by decomposing features into low- and high-frequency bands via FFT, applying intra- and inter-contrastive losses with adaptive modulators, and using the final layer as teacher for intermediate layers during diffusion denoising.
citing papers explorer
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A First-Principles Theory of Slow Thinking and Active Perception
Active lifting of data distributions via latent-sequence sampling and max-rate uncertainty reduction formally derives slow-thinking LLMs and places them on representation and sampler hierarchies that can be climbed.
-
Low-Pass Flow Matching
Low-Pass Flow Matching modifies Flow Matching via an operator-modulated interpolant inducing time-varying spectral bias from source spectrum to frequency-decaying bias, improving or preserving quality while reducing sampling cost on unconditional image generation including Galaxy10.
-
Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution
SKILD unifies unconditional image generation and continuous super-resolution in one diffusion model via scale-invariant k-space dynamics where the reverse process handles both tasks by varying only the starting timestep.
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Hyper-DP3: Frequency-Aware Right-Sizing of 3D Diffusion Policies for Visuomotor Control
HDP3 is a pocket-scale 3D diffusion policy with a Diffusion Mixer decoder that achieves state-of-the-art visuomotor control using two-step DDIM inference and under 1% of the parameters of prior 3D diffusion policies.
-
CSFlow: Aligning Flow Matching with Human Contrast Sensitivity
CSFlow derives inference-time timestep weights for flow matching by matching per-step frequency content to human CSF, yielding 4.7% FID reduction and smaller gains on IS and GenEval.
-
Colored Noise Diffusion Sampling
CNS is a plug-and-play stochastic sampler for diffusion models that uses timestep- and frequency-dependent colored noise to allocate energy to unresolved bands, producing lower FID scores than standard ODE/SDE baselines on ImageNet-256.
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Frequency-Guided Action Diffusion via Sub-Frequency Manifold Traversal
FGO guides diffusion policy generation via expanding spectral bands on sub-frequency manifolds to improve action smoothness on 15 robotic manipulation tasks.
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SpectralDiT: Timestep-Conditioned Spectral Residual Correction for Flow-Matching DiTs
SpectralDiT adds timestep-conditioned spectral residual correction to flow-matching DiTs and reports FID reductions of 5% on CIFAR-10 and 8.7% relative on ImageNet-100 latent diffusion with under 2% added parameters.
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HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation
HyFAD combines sequential time-to-frequency diffusion with frequency-aware step embeddings to achieve claimed state-of-the-art time series imputation on benchmarks.
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Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection
Flicker-DDPM accelerates DDPM sampling by injecting 1/f colored noise matched to image spectra, achieving similar quality with 3.33 times fewer steps on CIFAR-10.
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Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identification
DSFM generates synthetic fMRI time series via DWT-DCT dual transforms and spectral flow matching to improve downstream brain network classification.
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Spectral Progressive Diffusion for Efficient Image and Video Generation
Spectral Progressive Diffusion progressively grows resolution during denoising of pretrained diffusion models via spectral noise expansion and a power-spectrum-derived schedule, enabling training-free speedups and a fine-tuning recipe.
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FREE-Switch: Frequency-based Dynamic LoRA Switch for Style Transfer
FREE-Switch dynamically switches LoRA adapters using frequency importance per diffusion step and adds semantic alignment to reduce content drift when merging specialized image generators.
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FRAMER: Frequency-Aligned Self-Distillation with Adaptive Modulation Leveraging Diffusion Priors for Real-World Image Super-Resolution
FRAMER improves real-world super-resolution by decomposing features into low- and high-frequency bands via FFT, applying intra- and inter-contrastive losses with adaptive modulators, and using the final layer as teacher for intermediate layers during diffusion denoising.