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Multiplicative Diffusion Models: Beyond Gaussian Latents

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
score-based diffusiongenerative modelingmultiplicative noisenon-Gaussian latent variablesconservative dynamicsheavy-tailed distributionsFokker–Planck equation
Abstract:

We introduce a new class of generative models based on multiplicative score-driven diffusion. In contrast to classical diffusion models that rely on additive Gaussian noise, our construction is driven by skew-symmetric multiplicative noise. It yields conservative forward-backward dynamics inspired by principles of physics. We prove that the forward process converges exponentially fast to a tractable non-Gaussian latent distribution, and we characterize this limit explicitly. A key property of our diffusion is that it preserves the distribution of data norms, resulting in a latent space that is inherently data-aware. Unlike the standard Gaussian prior, this structure better adapts to heavy-tailed and anisotropic data, providing a closer match between latent and observed distributions. On the algorithmic side, we derive the reverse-time stochastic differential equation and associated probability flow, and show that sliced score matching furnishes a consistent estimator for the backward dynamics. This estimation procedure is equivalent to maximizing an evidence lower bound (ELBO), bridging our framework with established variational principles. Empirically, we demonstrate the advantages of our model in challenging settings, including correlated Cauchy distributions and experimental fluid dynamics data (d=1024). Across these tasks, our approach more accurately captures extreme events and tail behavior than classical diffusion models, particularly in the low-data regime. Our results suggest that multiplicative conservative diffusions open a principled alternative to current score-based generative models, with strong potential for domains where rare but critical events dominate.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces a multiplicative score-driven diffusion framework using skew-symmetric noise, yielding conservative forward-backward dynamics and a non-Gaussian latent distribution that preserves data norm distributions. It resides in the 'Multiplicative Score-Based Diffusion Models' leaf, which contains only three papers total, indicating a relatively sparse and emerging research direction. This leaf sits within the broader 'Multiplicative Noise Diffusion Theory and Frameworks' branch, suggesting the work contributes to foundational theory rather than applied denoising or domain-specific tasks.

The taxonomy reveals neighboring theoretical directions including 'Adaptive and Learned Noise Processes' (two papers on learned noise schedules) and 'Linear Response and Divergence-Kernel Methods' (two papers on stochastic system analysis). The paper's focus on skew-symmetric multiplicative noise and conservative dynamics distinguishes it from adaptive noise approaches that optimize schedules via variational inference. Its emphasis on physics-inspired principles and explicit latent distribution characterization also diverges from purely data-driven noise learning, positioning it at the intersection of rigorous mathematical formulation and generative modeling.

Among twenty-three candidates examined across three contributions, none were found to clearly refute any claimed novelty. The core MSGM framework examined ten candidates with zero refutable overlaps, as did the theoretical convergence analysis. The sliced score matching equivalence to ELBO examined three candidates, also with no refutations. This suggests that within the limited search scope—focused on top semantic matches and citation expansion—the specific combination of skew-symmetric multiplicative noise, conservative dynamics, and norm-preserving latent structure appears distinctive, though the small candidate pool limits definitive conclusions.

Based on the limited literature search covering twenty-three candidates, the work appears to occupy a novel position within multiplicative diffusion theory, particularly in its physics-inspired formulation and explicit latent characterization. However, the sparse taxonomy leaf (three papers) and modest search scope mean this assessment reflects visible prior work rather than exhaustive field coverage. The analysis does not capture potential overlaps in broader diffusion literature or adjacent mathematical frameworks outside the examined candidates.

Taxonomy

Core-task Taxonomy Papers
38
3
Claimed Contributions
23
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: generative modeling with multiplicative noise diffusion. The field has evolved around several complementary directions. At the theoretical level, researchers have developed frameworks for multiplicative noise processes, exploring score-based formulations and alternative noise schedules that depart from standard additive Gaussian assumptions. Works such as Beta diffusion[9] and On trainable multiplicative noise[1] exemplify efforts to understand how multiplicative perturbations can be integrated into diffusion models. Meanwhile, application-oriented branches focus on image restoration and denoising, where multiplicative noise naturally arises in domains like ultrasound imaging and synthetic aperture radar. Algorithmic innovations address inference methods, sampling strategies, and hybrid noise schemes, while specialized applications extend these ideas to domain-specific challenges ranging from medical imaging to uncertainty quantification. Recent activity highlights contrasting emphases between purely theoretical explorations and practical deployment. Some studies investigate foundational properties of multiplicative processes, examining convergence guarantees and score matching under non-additive noise, whereas others prioritize empirical performance in tasks like speckle reduction or anomaly detection (e.g., AnoDDPM[3]). Multiplicative Diffusion Models[0] sits within the theoretical branch focused on multiplicative score-based diffusion models, closely aligned with Multiplicative score-based generative models[38] and sharing conceptual ground with Beta diffusion[9]. Compared to these neighbors, Multiplicative Diffusion Models[0] emphasizes rigorous score-based formulations for multiplicative noise, contrasting with Beta diffusion[9]'s focus on bounded support and alternative parameterizations. This positioning reflects ongoing debates about which noise structures best balance mathematical tractability, expressive power, and computational efficiency across diverse generative tasks.

Claimed Contributions

Multiplicative Score-based Generative Model (MSGM)

The authors propose a novel generative modeling framework where the forward diffusion process uses skew-symmetric multiplicative noise instead of additive Gaussian noise. This yields conservative dynamics that preserve data norm distributions and converge to a tractable non-Gaussian latent space.

10 retrieved papers
Theoretical analysis of multiplicative diffusion convergence and latent distribution

The authors establish theoretical results showing exponential convergence of the forward diffusion to a non-Gaussian latent distribution. They derive the Fokker-Planck equation, prove that norms remain constant while directions converge to uniform distribution on the sphere, and characterize the latent space explicitly.

10 retrieved papers
Sliced score matching equivalence to ELBO for multiplicative diffusion

The authors prove that sliced score matching for their multiplicative diffusion framework is equivalent to maximizing the evidence lower bound. This theoretical result (Theorem 3.4.1) bridges their approach with established variational principles and justifies their training procedure.

3 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Multiplicative Score-based Generative Model (MSGM)

The authors propose a novel generative modeling framework where the forward diffusion process uses skew-symmetric multiplicative noise instead of additive Gaussian noise. This yields conservative dynamics that preserve data norm distributions and converge to a tractable non-Gaussian latent space.

Contribution

Theoretical analysis of multiplicative diffusion convergence and latent distribution

The authors establish theoretical results showing exponential convergence of the forward diffusion to a non-Gaussian latent distribution. They derive the Fokker-Planck equation, prove that norms remain constant while directions converge to uniform distribution on the sphere, and characterize the latent space explicitly.

Contribution

Sliced score matching equivalence to ELBO for multiplicative diffusion

The authors prove that sliced score matching for their multiplicative diffusion framework is equivalent to maximizing the evidence lower bound. This theoretical result (Theorem 3.4.1) bridges their approach with established variational principles and justifies their training procedure.

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