In this paper, we are interested in obtaining answers to the following questions for particle flow filters: Can we provide a theoretical guarantee that particle flow filters give correct results such as unbiased estimates? Are particle flows stable and under what conditions? Can we have one particle flow filter, rather than multiple seemingly different ones? To answer these questions, we first derive a parameterized family of stochastic particle flow filters, in which particle flows are driven by a linear combination of prior knowledge and measurement likelihood information. We then show that several particle flows existing in the literature are special cases of this family. We prove that the particle flows are unbiased under the assumption of linear measurement and Gaussian distributions, and that estimates constructed from the stochastic flows are consistent. We further establish several finite time stability concepts for this new family of stochastic particle flows. The results reported in this paper represent a significant development toward establishing a theoretical foundation for particle flow filters.