The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity in solving this problem due to their ability to learn complex patterns from data and generalize across diverse conditions. Among these, early works used Proper Orthogonal Decomposition (POD). Then, Generative Adversarial Networks (GAN) became popular, although they still present challenges at training or produce blurry reconstructions. Single-step supervised models like the SwinIR excel in image super-resolution, but have not been that much applied in fluid sparse data reconstruction. Beyond, diffusion models have emerged as particularly powerful in generative tasks, producing high-quality samples by iteratively refining noisy inputs. In contrast to other methods, these generative models are capable of reconstructing the smallest scales of the fluid spectrum. In this work, we apply a novel sampling method for Denoising Diffusion Implicit Models (DDIMs) that enables the reconstruction of the samples by guiding the reverse process using the available sparse data. Furthermore, we test a conflict-free physics-informed training method to enforce the governing equations in the generated fields. To evaluate the effectiveness of our method, we conduct experiments on two- and three-dimensional turbulent flow data, including isotropic turbulence, channel flows and weather data. Our method consistently outperforms other methods, especially at recovering high wave-number components of the turbulent spectrum. A successful application of these techniques to numerical data paves the way for their use in challenging experimental settings, where other neural-network-based approaches falter.