TL;DR
This paper introduces Forward-only Diffusion (FoD), a simplified generative model that learns data generation through a single forward process, achieving state-of-the-art results efficiently and with analytical tractability.
Contribution
FoD is a novel forward-only diffusion approach that eliminates the need for backward diffusion, simplifying training and inference while maintaining high performance.
Findings
Achieves state-of-the-art results on image restoration tasks.
Enables efficient few-step sampling during inference.
Demonstrates versatility in image-conditioned generation.
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 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 state-of-the-art performance on…
Peer Reviews
Decision·Submitted to ICLR 2026
**(S1)**: Elegant formulation. A single, forward-only SDE for diffusion with the mean-reversion term is a neat formulation for image-restoration and conditional generation tasks. The mean-reversion term enables a state-dependent denoising process that dynamically adjusts to different corruption levels within an image. To me, this makes a lot of sense for conditional generation. **(S2)**: Tractability and flexibility. The SDE with mean-reversion in the diffusion term still yields a unique, tract
**(W1)**: Poor unconditional generation. The FID scores on CIFAR-10 (7.89 for FoD-SDE, 5.01 for FoD-ODE) are not competitive with standard forward-backward diffusion models (e.g., Score SDE @ 2.38) or even other forward-only ODE models like Rectified Flow (2.58). While noted as a limitation, this positions FoD as more a specialized method for conditional image generation tasks than as a general generative model. **(W2)**: Limited exploration of conditional image generation tasks. The paper mai
* The writing is easy to follow. * Using the proposed mean-reverting-style SDE for generative modeling looks novel to me.
* The claim about "simpler, single" diffusion process is somewhat unconvincing to me. According to the training algorithm and sampling procedure, the effort is almost the same as that of the diffusion models, and the training objective itself needs approximation. * Another main claim of the paper is that the proposed method can be viewed as a stochastic counterpart to flow matching. However, to me, it would be necessary to compare the established stochastic counterpart, known as diffusion bridge
The paper is well written. The authors effort to consider diffusion coefficients as state dependent although the implementation is weak.
1. It seems the authors misinterpretation of forward diffusion as backward. This can be observed from they actually started from $x_T$ ∼ $p_{data}$ to $x_0$ ∼$ p_{prior}$. The training step stated in the paper actually resembles the backward diffusion diffusion step in the conventional diffusion. There is not much different between this method in terms forward/backward as the diffusion itself is not a reason to stay on forward only as what we can see from GOUB. 2. P4. Line 178, as the author m
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Taxonomy
MethodsDiffusion
