StraightDP: Geometry-Aware Differential Privacy for Rectified-Flow Transformers

Direct Preference Optimization (DPO) is successful for alignment in LLMs but still faces challenges in text-to-image generation. Existing studies are confined to denoising diffusion models while overlooking flow-matching, and suffer from an objective mismatch when applying discrete NLP-based DPO to regression-based generative tasks.\ In this paper, we derive a generalized DPO objective that covers both diffusion and flow-matching via a unified reverse-time SDE framework, and point out from a gradient perspective that the standard DPO objective is suboptimal for text-to-image generation. Consequently, we propose Linear-DPO, which replaces the aggressive sigmoid-based utility function with a sustained linear utility and incorporates an EMA-updated reference model. Qualitative and quantitative experiments on diffusion models (SD1.5, SDXL) and flow-matching model (SD3-Medium) demonstrate the superiority of our approach over existing baselines.

Differentially private optimization suffers from a fundamental geometric mismatch: deep networks have highly anisotropic loss landscapes, yet DP-SGD injects isotropic noise. Second-order preconditioning can resolve this, but estimating curvature typically requires private data (consuming privacy budget) or public data (introducing distribution shift). We show that the Fisher Information Matrix decouples into architectural sensitivity, recoverable via synthetic noise, and input correlations, approximable from modality-specific frequency statistics. We propose DP-KFC, which constructs KFAC preconditioners by probing networks with structured synthetic noise, requiring neither private nor public data. Empirically, DP-KFC consistently outperforms DP-SGD and adaptive baselines across diverse modalities in strong privacy regimes ($\varepsilon \leq 3$). DP-KFC matches private-data preconditioners while public-data variants degrade by up to $4.8\%$, showing that curvature can be estimated without consuming privacy budget or introducing distribution shift. This enables privacy-preserving learning in specialized domains (e.g., medical applications) where regulatory constraints make data scarce.

Differentially private stochastic gradient descent (DP-SGD) enables private deep learning through per-example clipping and calibrated Gaussian noise, but its high-variance updates can reduce utility on challenging datasets. We propose \textbf{SMA-DP-SGD}, a \textbf{Spectral Memory-Aware Differentially Private Stochastic Gradient Descent} method that augments DP-SGD with a fractional memory branch built only from previously privatized noisy releases. WeightWatcher-inspired power-law spectral exponents provide group-wise reliability signals, instantiated layer-wise in our experiments, to adapt the decay and effective memory depth. Private-history alignment, norm matching, and warm-up activation stabilize the memory contribution. Privacy remains transparent: conditioned on the private release history, the memory branch is fixed, and the only newly data-dependent term is the current clipped sum scaled by a fixed coefficient $β$. Hence, SMA-DP-SGD preserves a clean conditional sensitivity structure and exactly recovers group-wise DP-SGD when $β=1$. Experiments on CIFAR-100, CIFAR-10, and MNIST show competitive or superior accuracy over several DP optimization baselines, with the largest gains on CIFAR-100 and CIFAR-10. CIFAR-10 ablations show that $β$ controls the privacy--utility trajectory, while spectral and memory diagnostics confirm a controlled short-to-moderate effective memory depth and a small memory-branch ratio. Runtime analysis shows that the mechanism incurs additional overhead, about $2.94\times$ DP-SGD in our CIFAR-10 implementation, revealing a practical trade-off between adaptive private memory and computational cost.