Forward-only Diffusion Probabilistic Models

• URL: http://arxiv.org/abs/2505.16733v1
• Date: Thu, 22 May 2025 14:47:07 GMT
• Title: Forward-only Diffusion Probabilistic Models
• Authors: Ziwei Luo, Fredrik K. Gustafsson, Jens Sjölund, Thomas B. Schön,
• Abstract summary: This work presents a forward-only diffusion (FoD) approach for generative modelling.<n>FoD directly learns data generation through a single forward diffusion process.<n>FoD is analytically tractable and is trained using a simple flow matching objective.
• Score: 14.538117998129307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work presents a forward-only diffusion (FoD) approach for generative modelling. In contrast to traditional diffusion models that rely on a coupled forward-backward diffusion scheme, FoD directly learns data generation through a single forward diffusion process, yielding a simple yet efficient generative framework. The core of FoD is a state-dependent linear stochastic differential equation that involves a mean-reverting term in both the drift and diffusion functions. This mean-reversion property guarantees the convergence to clean data, naturally simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling a few-step non-Markov chain sampling during inference. The proposed FoD model, despite its simplicity, achieves competitive performance on various image-conditioned (e.g., image restoration) and unconditional generation tasks, demonstrating its effectiveness in generative modelling. Our code is available at https://github.com/Algolzw/FoD.

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