Deterministic Dynamics of Sampling Processes in Score-Based Diffusion Models with Multiplicative Noise Conditioning
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the sampling process, previous work by Song and Ermon (2020) demonstrated that neural networks using multiplicative noise conditioning can still generate satisfactory samples. In this setup, the model is expressed as the product of two functions: one depending on the spatial variable and the other on the noise magnitude. This structure limits the model's ability to represent a more general relationship between the spatial variable and the noise, indicating that it cannot fully learn the correct score. Despite this limitation, the models perform well in practice. In this work, we provide a theoretical explanation for this phenomenon by studying the deterministic dynamics of the associated differential equations, offering insight into how the model operates.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 8 of its 15 references that are in the map. First posted on arXiv 19 Jan 2026.
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8 of 15 references.
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- 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
- 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
- 2020Improved Techniques for Training Score-Based Generative Models16 Jun
Other references · 3
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
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