Regularization can make diffusion models more efficient
Mahsa Taheri, Johannes Lederer
TL;DR
This paper demonstrates that applying sparsity to diffusion models can significantly reduce computational costs while improving sample quality, making these models more efficient for generative AI applications.
Contribution
It introduces a sparsity-based approach with mathematical guarantees that reduce computational complexity and empirically improves sample quality in diffusion models.
Findings
Sparsity reduces the influence of input dimension on complexity.
Inducing sparsity leads to better sample quality.
Sparsity achieves these improvements at lower computational costs.
Abstract
Diffusion models are one of the key architectures of generative AI. Their main drawback, however, is the computational costs. This study indicates that the concept of sparsity, well known especially in statistics, can provide a pathway to more efficient diffusion pipelines. Our mathematical guarantees prove that sparsity can reduce the input dimension's influence on the computational complexity to that of a much smaller intrinsic dimension of the data. Our empirical findings confirm that inducing sparsity can indeed lead to better samples at a lower cost.
Peer Reviews
Decision·Submitted to ICLR 2026
The addition of an explicit L^1 regularization to the score-matching objective, and a guarantee on sampling iteration complexity depending on the sparsity of the score functions is interesting -- it's further interesting that the new objective does seem to give reasonable results on (very) small-scale experiments. The fact that the new objective provides a reasonable approximation to the score even in the absence of sparsity is a plus. The paper itself is easy to read, and the contributions are
From a technical perspective, the theory seems to largely be a rehashing of previous results with some modifications. The empirical results are unfortunately too small-scale to be convincing to practitioners -- even the CIFAR experiments included in the appendix were run using a non-standard 32 channel network instead of the standard 128 channels. Additionally, it's not clear how the regularization parameter $r$ should be set in practice, and for instance, how sensitive the results are to this
The paper provides detailed explanations for each assumption and theorem, offering clear intuition behind the proposed method. The theoretical derivations are comprehensive and rigorous, establishing a solid foundation for the concept of regularized score-based diffusion models.
1. The paper does not provide code or implementation details, making it difficult to assess the practical feasibility of the method. Moreover, there is no analysis of the hyperparameters $s,r,\kappa$, leaving the experimental section incomplete. 2. From the presented results, the method only shows effectiveness on datasets with inherently sparse structures, such as MNIST. Even for MNIST, where sparsity is visually evident, the sparsity-inducing SGM struggles to generate high-quality samples wit
1. Provides a clear theoretical link between sparsity regularization and improved non-asymptotic convergence, reducing dimensional dependence from $d$ to $s$. 2. The proposed regularized score-matching objective is simple to implement and compatible with existing diffusion frameworks
The main theoretical guarantee hinges on the unverified assumption that the true score function is s-sparse, and given the experiments are limited to low-dimensional datasets, it remains unclear whether the same efficiency extends to large-scale diffusion models.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering
MethodsDiffusion