Using the participle and using the infinitive have different meanings.
The infinitive can be used with verbs such as "(mit)kommen", "gehen", "fahren" to mean "come/go to do something", that is, that you do a movement in order to go to a place where you can do something.
Kommst du heute mit schwimmen?
Are you coming to swim with me?
This construction can be used with any kind of activity and is very common.
The participle specifies the means of coming. It is therefore only possible with intransitive verbs that imply a motion, for example with "heraussprudeln" or "schwimmen". It is also exclusively used with "kommen", not with other verbs of motion.
Marlene kommt geschwommen.
Marlene comes swimming
Often a form already implying a motion towards the speaker is used, with "her" or "an".
Marlene kommt angeschwommen
Note that there is no verb "anschwimmen" (at least not with that meaning), the "an" comes from the construction.
The focus is on "coming", but it is also specifying the means. That is why
is sounds strange in pleas or questions. For example in
*Kommst du geschwommen?
"geschwommen" is superfluous. If "schwimmen" was the focus, one would say
Schwimmst du hierher?
The focus on coming is why this construction is used a lot in plays and stories. Characters enter the stage, and while the focus is on them entering, the means is also conveyed.