Here is a short list on variations on the design thinking process.
The first process can be found on webpages at the d.school at Stanford. We see several stages, with variating degree in intensity: Empathize, Define, Ideate, Prototype, Test and Iterate.
The process starts with reflections on whom to work for, exploring and selecting perspectives, reflections on learning outcomes and prototyping, as well as evaluation of prototypes.
Next, there is a circular model proposed by Tim Brown of Ideo.
Here, we see that Inspiration influences ideation and implementation and vice-versa.
An iterative design thinking process that is taught at TU Munich Business School is shown below:
Here, we start with an analysis phase, a design phase follows, a prototype is build. Then, there is play and review on the experiences.
An approach called "customer journey" to service design can be found here. It is also a circular model, starting with a "pre-service" period, a service period, and a post-service period.
Another circular model to design thinking is given by Prof. Ranjan from India. He calls his model the "hand-heard-head" model of design.
Design of 1st order is about form and function. Design on 2nd order is about Function, Feeling, impact and effect. Design of 3rd order is about Meaning and Purpose.
Still farther East, I. Nonaka proposes a model for innovation and learning that is somewhat similar to design thinking. It is the SECI model of knowledge creation. Nonaka starts with the aspect of empathy and observation, that he calls "socialisation". Here, knowledge that is difficult to articulate is experienced. Then, the implicit knowledge is made explicit by the process of "externalisation". This is mainly about codification of experiences with symbols or models. Third, externalised knowledge is combined in new ways to generate new concepts and ideas. This is called "combination". Last is the process of internalisation, where explicit knowledge is converted again into implicit knowledge in the form of best practices.
A short overview on design-thinkers can be found here.