As you may be able to gleam from their names, Dyson has a handful of fans that are also air purifiers. Out of the entire Dyson fan range, three of the five also have an air purifying element to them and one is also a fan heater.
Every one of Dyson's air purifying fans uses a HEPA 13 filter that is rated to remove 99.95% of particulate matter from the air. This rating makes them medical grade, and can help clear out dangerous PM2.5 particles from your home. Two are also rated to remove formaldehyde which is a polluting gas that can come from things like paint, nail polish remover, air fresheners, and a range of other household items.
The entry level purifying fan is the Dyson Purifier Cool. Aside from its HEPA filter this device also has an activated carbon filter which can help remove odours from the home. It oscillates up to 350° and can circulate 290L/s of air on fan mode. According to Dyson it is able to effectively purify air in rooms up to 81m cubed, which is around a 6m x 6m room with an average height ceiling.
A step up from that is the Dyson Purifier Cool Formaldehyde purifying fan. For all intents and purposes this is the same fan as the Purifier Cool, except it has a catalytic filter that breaks down formaldehyde molecules. It can also circulate more air that the previous model with the airflow amping up to 370L/s.
The most advanced Dyson purifying fan is the Dyson Purifier Hot+Cool Formaldehyde purifying fan. It sure is a mouthful, but the differences aren't. On top of everything from the Dyson Purifier Cool Formaldehyde, you also get heating elements but the airflow is back down to 290L/s.