Updated to address comments.
If Project XYZ is simply a funding agency or entity that may have provided funds or materials but no intellectual contribution, then you use the phrase "We acknowledge Agency XYZ (Grant #) for financial support" or "Funding provided through Project XYZ (Grant #)." For example, if your work is supported by a grant from the National Institutes of Health...
"Funding for this work was provided by the NIH, Center for Work on Really Interesting Science (#1234567890)..."
If project XYZ has defined the research problem/scope, you could say "This research was inspired by Project XYZ" or "This research follows from Porject XYZ."
If Project XYZ is an institute, center, or other entity that worked with you on your project, then you use the phase "in collaboration with". For example, if your computational model was run on at the Pittsburgh Supercomputing Center, you might say:
"This work was conducted in collaboration with the Pittsburgh Supercomputing Center [ref]..."
Lastly, if the intellectual contribution from someone at Project XYZ was large, that person needs to have their name on your paper (with placement in the order according to the customs of your field):
Grad Student who did the work*, Grad Student who did less work*, Grad Student at Project XYZ#, Collaborating PI at Project XYZ#, Your PI*
*Department of Epic Awesome, University of Cool, 123 Street Road, CityTown,
ProvinceState, CountryNation, ComplicatedPostalCode.
#Center for Statistical Mayhem, International Project for
Enhancing Statistical Literacy through Academic Research, 456 Boulevard Ave,
CityTown, ProvinceState, CountryNation, ComplicatedPostalCode.