Robust fine-tuning aims to adapt large foundation models to downstream tasks while preserving their robustness to distribution shifts. Existing methods primarily focus on constraining and projecting current model towards the pre-trained initialization based on the magnitudes between fine-tuned and pre-trained weights, which often require extensive hyper-parameter tuning and can sometimes result in underfitting. In this work, we propose Drectional Grdient Projection (DiGraP), a novel layer-wise trainable method that incorporates directional information from gradients to bridge regularization and multi-objective optimization. Besides demonstrating our method on image classification, as another contribution we generalize this area to the multi-modal evaluation settings for robust fine-tuning. Specifically, we first bridge the uni-modal and multi-modal gap by performing analysis on Image Classification reformulated Visual Question Answering (VQA) benchmarks and further categorize ten out-of-distribution (OOD) VQA datasets by distribution shift types and degree (i.e. near versus far OOD). Experimental results show that DiGraP consistently outperforms existing baselines across Image Classfication and VQA tasks with discriminative and generative backbones, improving both in-distribution (ID) generalization and OOD robustness.