This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis for different types of mechanisms, since for example, images are formed from a collection of pixels, which themselves could be generated from a four-bar or six-bar. Path synthesis problems have generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitted solutions to particular precision points. However, most kinematic synthesis problems are concept generation problems, where a designer cares more about generating a large number of plausible solutions, which could reach given precision points only approximately. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve. This approach is also conducive to implementation for pressure-sensitive touch-based design interfaces, where the input is not a zero-thickness curve, but the sweep of a small patch on the finger.