This paper introduces gradient guidance for adapting and fine-tuning diffusion models towards user-specified optimization objectives. We study the theoretical aspects of a guided score-based sampling process, linking gradient-guided diffusion models to first-order optimization. We show that adding gradient guidance to the sampling process of a pre-trained diffusion model is equivalent to solving a regularized optimization problem, where the regularization term acts as a prior determined by the pre-training data. Diffusion models can learn data's latent subspace, but adding the gradient of an external objective function to the sampling process risks disrupting the structure in generated samples. To address this, we propose a modified form of gradient guidance based on a forward prediction loss, which preserves the latent structure in generated samples. We further consider an iteratively fine-tuned version of gradient-guided diffusion, where gradients are queried at newly generated data points and the score network is updated using new samples. This process mimics a first-order optimization iteration, with a convergence rate of $ \mathcal{O}(1/K) $ to the global optimum when the objective function is concave. We investigate the role of guidance in diffusion models from an optimization perspective. The goal is to generate samples that optimize a given objective function $ f $. Drawing inspiration from gradient-based optimization methods, we construct a guidance signal based on the gradient vector $ \nabla f $. We use this gradient signal, along with the pre-trained score function, to guide the sampling process towards generating structured output with higher function values. Our main results show that gradient guidance preserves the latent subspace structure of the data and ensures fast convergence towards the optimal solution. We also provide theoretical guarantees for the convergence of gradient-guided diffusion models to regularized optima, demonstrating that the generated samples converge to a solution that is regularized with respect to the original problem. The regularization ensures that the generated samples remain proximal to the training data, revealing a fundamental limit for adapting pre-trained diffusion models. We further show that an adaptive variant of gradient-guided diffusion, where both the score function and gradient guidance are iteratively fine-tuned, converges to global optima within the latent subspace at a rate of $ \mathcal{O}(1/K) $.This paper introduces gradient guidance for adapting and fine-tuning diffusion models towards user-specified optimization objectives. We study the theoretical aspects of a guided score-based sampling process, linking gradient-guided diffusion models to first-order optimization. We show that adding gradient guidance to the sampling process of a pre-trained diffusion model is equivalent to solving a regularized optimization problem, where the regularization term acts as a prior determined by the pre-training data. Diffusion models can learn data's latent subspace, but adding the gradient of an external objective function to the sampling process risks disrupting the structure in generated samples. To address this, we propose a modified form of gradient guidance based on a forward prediction loss, which preserves the latent structure in generated samples. We further consider an iteratively fine-tuned version of gradient-guided diffusion, where gradients are queried at newly generated data points and the score network is updated using new samples. This process mimics a first-order optimization iteration, with a convergence rate of $ \mathcal{O}(1/K) $ to the global optimum when the objective function is concave. We investigate the role of guidance in diffusion models from an optimization perspective. The goal is to generate samples that optimize a given objective function $ f $. Drawing inspiration from gradient-based optimization methods, we construct a guidance signal based on the gradient vector $ \nabla f $. We use this gradient signal, along with the pre-trained score function, to guide the sampling process towards generating structured output with higher function values. Our main results show that gradient guidance preserves the latent subspace structure of the data and ensures fast convergence towards the optimal solution. We also provide theoretical guarantees for the convergence of gradient-guided diffusion models to regularized optima, demonstrating that the generated samples converge to a solution that is regularized with respect to the original problem. The regularization ensures that the generated samples remain proximal to the training data, revealing a fundamental limit for adapting pre-trained diffusion models. We further show that an adaptive variant of gradient-guided diffusion, where both the score function and gradient guidance are iteratively fine-tuned, converges to global optima within the latent subspace at a rate of $ \mathcal{O}(1/K) $.