Time Series Diffusion in the Frequency Domain

• URL: http://arxiv.org/abs/2402.05933v1
• Date: Thu, 8 Feb 2024 18:59:05 GMT
• Title: Time Series Diffusion in the Frequency Domain
• Authors: Jonathan Crabb\'e, Nicolas Huynh, Jan Stanczuk, Mihaela van der Schaar
• Abstract summary: We analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. We show that a dual diffusion process occurs in the frequency domain with an important nuance. We show how to adapt the denoising score matching approach to implement diffusion models in the frequency domain.
• Score: 54.60573052311487
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brownian motions are replaced by what we call mirrored Brownian motions, characterized by mirror symmetries among their components. Building on this insight, we show how to adapt the denoising score matching approach to implement diffusion models in the frequency domain. This results in frequency diffusion models, which we compare to canonical time diffusion models. Our empirical evaluation on real-world datasets, covering various domains like healthcare and finance, shows that frequency diffusion models better capture the training distribution than time diffusion models. We explain this observation by showing that time series from these datasets tend to be more localized in the frequency domain than in the time domain, which makes them easier to model in the former case. All our observations point towards impactful synergies between Fourier analysis and diffusion models.

Related papers

• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• Boosting Diffusion Models with Moving Average Sampling in Frequency Domain [101.43824674873508]
  Diffusion models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)"
  arXiv  Detail & Related papers  (2024-03-26T16:57:55Z)
• Diffusion-TS: Interpretable Diffusion for General Time Series Generation [6.639630994040322]
  Diffusion-TS is a novel diffusion-based framework that generates time series samples of high quality. We train the model to directly reconstruct the sample instead of the noise in each diffusion step, combining a Fourier-based loss term. Results show that Diffusion-TS achieves the state-of-the-art results on various realistic analyses of time series.
  arXiv  Detail & Related papers  (2024-03-04T05:39:23Z)
• Particle Denoising Diffusion Sampler [32.310922004771776]
  Particle Denoising Diffusion Sampler (PDDS) provides consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks.
  arXiv  Detail & Related papers  (2024-02-09T11:01:35Z)
• Guided Diffusion from Self-Supervised Diffusion Features [49.78673164423208]
  Guidance serves as a key concept in diffusion models, yet its effectiveness is often limited by the need for extra data annotation or pretraining. We propose a framework to extract guidance from, and specifically for, diffusion models.
  arXiv  Detail & Related papers  (2023-12-14T11:19:11Z)
• To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models [20.315727650065007]
  Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. We leverage known connections to control akin to the F"ollmer drift to extend established neural network approximation results for the F"ollmer drift to denoising diffusion models and samplers.
  arXiv  Detail & Related papers  (2023-05-16T16:56:19Z)
• Denoising Diffusion Samplers [41.796349001299156]
  Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. We explore a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling.
  arXiv  Detail & Related papers  (2023-02-27T14:37:16Z)
• Diffusion Models in Vision: A Survey [80.82832715884597]
  A diffusion model is a deep generative model that is based on two stages, a forward diffusion stage and a reverse diffusion stage. Diffusion models are widely appreciated for the quality and diversity of the generated samples, despite their known computational burdens.
  arXiv  Detail & Related papers  (2022-09-10T22:00:30Z)
• First Hitting Diffusion Models [19.19644194006565]
  First Hitting Diffusion Models (FHDM) generate data with a diffusion process that terminates at a random first hitting time. We observe considerable improvement compared with the state-of-the-art approaches in both quality and speed.
  arXiv  Detail & Related papers  (2022-09-02T17:01:32Z)
• How Much is Enough? A Study on Diffusion Times in Score-based Generative Models [76.76860707897413]
  Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution. We show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process.
  arXiv  Detail & Related papers  (2022-06-10T15:09:46Z)

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.