Good Morning,
Most astilbe are propagated by division, but some are by
seed.
Spring is a great time to divide established plants that you might already have in the garden. At this time of year they’re just starting off into growth and are raring to go, so should settle down and grow away nicely after you’ve divided them.

• Just dig up the plant, getting all of the roots. With more established plants you may need to use hand forks, garden forks, or even a sharp spade to divide them.
• Shake off excess oil to expose more of the roots and better see the plant.
• Get your hands in there and divide the clump into several pieces. Each section needs to have its own shoots.
• Replant in a space that is amended with some compost and perhaps a little slow-release organic fertilizer. Or pot up the small herb starts into large containers filled with a soil-based potting mix to grow them on a bit before giving them away to gardening friends.

For seed propagation, sow seeds in the light at 63°-70°F (17°-21°C). Germination will occur in 7-14 days. Plugs (with 3-4 leaves) are ready for shipping or transplanting into larger containers in 8-10 weeks.

Astilbe Flowers: Planting, Growing, and Caring for Astilbes (almanac.com)
perennial_forcing_astilbe_1998_ocr.pdf (plantgrower.org)

I hope this helps.  Thanks for using our service.