Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization

Text-to-image diffusion models have achieved remarkable generative capabilities, yet accurately aligning complex textual prompts with synthesized layouts remains an ongoing challenge. In these models, the initial Gaussian noise acts as a critical structural seed dictating the macroscopic layout. Recent online optimization and search methods attempt to refine this noise to enhance text-image alignment. However, relying on unconstrained Euclidean gradient ascent mathematically inflates the latent norm and destroys the standard Gaussian prior, causing severe visual artifacts like color over-saturation. Furthermore, these methods suffer from inefficient semantic routing and easily fall into the ``reward hacking'' trap of external proxy models. To address these intertwined bottlenecks, we propose Oracle Noise, a zero-shot framework reframing noise initialization as semantic-driven optimization strictly confined to a Riemannian hypersphere. Instead of relying on complex external parsers, we directly identify the most impactful structural words in the prompt to efficiently route optimization energy. By updating the noise strictly along a spherical path, we mathematically preserve the original Gaussian distribution. This geometric constraint eliminates norm inflation and unlocks aggressive step sizes for rapid convergence. Extensive experiments demonstrate that Oracle Noise significantly accelerates semantic alignment and achieves superior aesthetics without black-box models. It completely mitigates Euclidean-induced degradation, establishing state-of-the-art performance across human preference metrics (e.g., HPSv2, ImageReward), semantic alignment (CLIP Score), and sample diversity, all within a strict 2-second optimization budget.

$Z^2$-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models

Diffusion models have achieved unprecedented success in text-aligned generation, largely driven by Classifier-Free Guidance (CFG). However, standard CFG operates strictly on instantaneous gradients, omitting the intrinsic curvature of the data manifold. Recent methods like Zigzag-sampling (Z-Sampling) explicitly traverse multi-step forward-backward trajectories to probe this curvature, significantly improving semantic alignment. Yet, these explicit traversals triple the Neural Function Evaluation (NFE) cost and introduce unconstrained truncation errors from off-manifold evaluations, causing cumulative drift from the true marginal distribution. In this paper, we theoretically demonstrate that the explicit zigzag sequence is topologically reducible. We propose Implicit Z-Sampling, rigorously proving that intermediate states can be algebraically annihilated via operator dualities, physically eliminating off-manifold approximation errors. To push sampling efficiency to its theoretical lower bound, we introduce $Z^2$-Sampling (Zero-cost Zigzag Sampling). Exploiting the Probability Flow ODE's temporal coherence, $Z^2$-Sampling couples implicit algebraic collapse with a dynamically cached Temporal Semantic Surrogate. This restores the standard 2-NFE baseline without sacrificing semantic exploration. We formally prove via Backward Error Analysis that this discrete collapse inherently synthesizes a directional derivative curvature penalty. Finally, extensive evaluations demonstrate that $Z^2$-Sampling structurally shatters the performance-efficiency Pareto frontier. We validate its universal applicability across diverse architectures (U-Nets, DiTs) and modalities (image/video), establishing seamless orthogonality with advanced alignment frameworks (AYS, Diffusion-DPO).

Guided Path Sampling: Steering Diffusion Models Back on Track with Principled Path Guidance

Iterative refinement methods based on a denoising-inversion cycle are powerful tools for enhancing the quality and control of diffusion models. However, their effectiveness is critically limited when combined with standard Classifier-Free Guidance (CFG). We identify a fundamental limitation: CFG's extrapolative nature systematically pushes the sampling path off the data manifold, causing the approximation error to diverge and undermining the refinement process. To address this, we propose Guided Path Sampling (GPS), a new paradigm for iterative refinement. GPS replaces unstable extrapolation with a principled, manifold-constrained interpolation, ensuring the sampling path remains on the data manifold. We theoretically prove that this correction transforms the error series from unbounded amplification to strictly bounded, guaranteeing stability. Furthermore, we devise an optimal scheduling strategy that dynamically adjusts guidance strength, aligning semantic injection with the model's natural coarse-to-fine generation process. Extensive experiments on modern backbones like SDXL and Hunyuan-DiT show that GPS outperforms existing methods in both perceptual quality and complex prompt adherence. For instance, GPS achieves a superior ImageReward of 0.79 and HPS v2 of 0.2995 on SDXL, while improving overall semantic alignment accuracy on GenEval to 57.45%. Our work establishes that path stability is a prerequisite for effective iterative refinement, and GPS provides a robust framework to achieve it.