FRPSS: Feature Rearrangement in Pre-Shape Space for Single-Image Generation

Generative modeling and self-supervised representation learning (SSL) optimize structurally different objectives: generative training rewards distributional fidelity, while SSL rewards semantic coherence. Yet recent work repeatedly finds that SSL features improve generative training, though the mechanism of this synergy remains unclear. Here, we study the benefits of SSL in generative modeling in the framework of one-step generation where the role of representation is explicit: frozen SSL features are used to match generated samples to real data. We use the Sinkhorn divergence in that feature space, providing a tractable surrogate for the Wasserstein distance, the population-level discrepancy approximated by Fréchet-style evaluation metrics (such as FID). We find that this objective becomes highly effective when computed in a semantically structured SSL feature space (a 39$\times$ reduction in ImageNet FID). We trace this behavior primarily to matching estimation: semantic SSL features that suppress nuisance reconstruction details induce a more compact geometry, making distribution matching more tractable. As a consequence, the best training SSL features need not match the features used by the evaluation metric. In particular, we show that using Inception as the feature extractor can improve FID while degrading matching stability and sample quality, revealing a form of metric hacking. Using extensive experiments on ImageNet, we identify which SSL feature families lead to best generation performance and show that matching stability is a quantitative criterion for selecting them. Code is available at https://github.com/Genentech/semantic-transport-generation.

We consider the problem of generating images whose internal structure -- defined by the distribution of patches across multiple scales -- matches that of a single reference image. Recent approaches address this problem by training a diffusion model on a single image. But even in this setting, training is computationally expensive and requires hours of optimization. Instead, we model the image using a dataset of its patches at different scales. As this dataset is finite and the dimensionality of its patches is small, the score function for a noisy patch can be computed tractably using an optimal, closed-form denoiser, eliminating the need for neural network training. We integrate this patch-based denoiser into an efficient, training-free image diffusion model, and we describe how our method connects to classical patch-based image restoration techniques. Our approach achieves state-of-the-art generation quality and diversity compared to trained single-image diffusion models, and we demonstrate applications, including unconditional image generation, text-guided stylization, image symmetrization, and retargeting. Further, we show that our approach is compatible with latent space diffusion, and we show multiple additional acceleration techniques to achieve megapixel single-image generation in one second, and gigapixel generation in minutes.

While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce \textbf{SE-UNet} (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.