Digital twins rely on accurate and efficient probabilistic inference to assimilate data, quantify uncertainty, and update high-fidelity models of complex physical systems. These tasks often require sampling from high-dimensional, strongly non-Gaussian, and multimodal posterior distributions, posing significant challenges for existing particle-based methods. While kernel-based particle flows such as the Kernel Fisher–Rao (KFR) flow provide flexible, gradient-free sampling strategies, they can suffer from poor multimodal coverage due to the limitations of geometric interpolation between prior and posterior distributions. We develop a deterministic particle flow framework based on the convolutional path, a smoother and more gradual interpolation that is better suited for complex posterior landscapes. The convolutional path, commonly used in diffusion-based sampling, mitigates the mass “beaming” effect of geometric paths and is therefore particularly attractive for digital twin applications, where maintaining multiple competing hypotheses is essential. We formulate the particle evolution as an interacting particle system governed by a velocity field derived from a Poisson equation associated with the convolutional path. To enable practical computation, we adopt a flexible Galerkin projection framework, generalizing existing kernel-based approaches and allowing the use of structured particle sets such as quasi-Monte Carlo points or sparse grids. Unlike classical KFR flows, the proposed approach incorporates gradient information of the prior and target models, trading gradient-free operation for improved robustness in multimodal settings. The focus of this contribution is on the theoretical formulation, Monte Carlo approximations, and implementation strategy of the proposed flow. Ongoing work aims to analyze stability, computational cost, and effectiveness in representative digital twin scenarios involving multimodal uncertainty. This project outlines a promising direction for particle flow methods tailored to the demands of next-generation digital twin systems.