Exhibit 23.2

CONSENT OF INDEPENDENT ACCOUNTING FIRM

We consent to use in this Registration Statement on Form S-4 of Vital Therapies, Inc. of our report dated January 30, 2019, with respect to the audited consolidated financial statements of Immunic AG as of December 31, 2017 and 2016 and for the years then ended.

We also consent to the references to us under the heading “Experts” in such Registration Statement.

/s/ Baker Tilly GmbH & Co. KG

Baker Tilly GmbH & Co. KG Wirtschaftsprüfungsgesellschaft (Düsseldorf)

Munich, Germany

February 14, 2019