Ovens and indoor air quality

The PM2.5 air quality index (AQI) is a big deal where I live (China). The outdoor air is monitored in all major cities and activities are often planned around the current AQI. It's a lot easier to control indoor air quality than outdoor air quality. You can reduce indoor PM2.5 by 95% with a good HEPA-filter air purifier. For these reasons, I'm reluctant to introduce anything indoors that may compromise indoor AQI. Sometimes the AQI from people smoking indoors is worse than the AQI outdoors.

Is it possible to have completely clean air with a wood-fired oven indoors? I know it depends on the design of the flue and chimney, but even with the best design won't some particulate pollution enter the room?

I've also been looking at propane-fueled gas ovens. These also require ventilation. I've seen these in restaurants without a chimney. Instead, there is a wide PVC pipe that runs out the side of the building horizontally. Propane burns a lot cleaner than wood, but it will produce carbon monoxide and some soot.

Electric ovens are the cleanest option but they cost the most to operate. Propane is very cheap and may cost only 1/3 of what an equivalent electric oven costs to operate. Wood is likely the cheapest, although it will have to be hauled in from nearby villages.