1. Sexually through seeds:

* Pollination: Peonies are pollinated by insects like bees and butterflies. Pollen from the male part (stamen) of one flower is transferred to the female part (pistil) of another flower.

* Fertilization: After pollination, the pollen fertilizes the ovules in the ovary, forming seeds.

* Seed development: The ovary develops into a seed pod containing multiple seeds.

* Germination: Peony seeds need a period of cold stratification (exposure to cold temperatures) before they can germinate. This usually takes several months. Once the seeds are planted in the ground, they will sprout into new plants.

2. Asexually through division:

* Division: This is the most common method of propagation for peonies.

* Process: Mature peony plants can be divided into multiple smaller plants with their own root system.

* Timing: Division is usually done in the fall or early spring.

* Advantages: This method ensures that the new plants are genetically identical to the parent plant and will produce flowers of the same variety. It also results in faster flowering than growing from seeds.

Here's a breakdown of the differences:

* Sexual reproduction (seeds): Creates genetically diverse offspring, with potential for new traits, but slower flowering.

* Asexual reproduction (division): Creates genetically identical offspring, preserving desired traits, and faster flowering.

While peonies can reproduce through seeds, it's generally not the preferred method for gardeners because of the long time it takes for seeds to germinate and bloom. Most gardeners choose to propagate peonies through division for faster results and guaranteed similar flower characteristics.