Inclusion Criteria:

1. Histologically or cytologically confirmed chronic myelogenous leukemia, acute myeloid leukemia, acute lymphocytic leukemia, multiple myeloma, Waldenstrom's macroglobulinemia, non-Hodgkin's lymphoma or Hodgkin's disease.
2. Patients must be refractory to, intolerant of, or decline to receive established therapy known to provide clinical benefit for their condition.
3. Age > 18 years
4. ECOG performance score of 0 or 1
5. Adequate renal function as evidenced by serum creatinine < 2.0 mg/dL

6. Adequate hepatic function as evidenced by:

   • Serum total bilirubin < 2.0 mg/dL (Patients with known Gilbert's syndrome may have total bilirubin values of up to 3 mg/dL.)
   • Alkaline phosphatase < 3X the upper limit of normal (ULN) for the reference lab (< 5X the ULN if considered related to underlying disease)
   • SGOT/SGPT < 3X the ULN for the reference lab (< 5X the ULN if considered related to underlying disease
7. Patients must be recovered from the clinically significant effects of any prior surgery, radiotherapy or other antineoplastic therapy.
8. Patients or their legal representatives must be able to read, understand and provide written informed consent to participate in the trial.
9. Women of childbearing potential as well as fertile men and their partners must agree to use an effective form of contraception during the study and for 90 days following the last dose of study medication (an effective form of contraception is an oral contraceptive or a double barrier method).

Exclusion Criteria:

1. Patients with an uncontrolled active infection
2. Prior treatment with an inosine-5-monophosphate dehydrogenase (IMPDH)-inhibitor
3. History of prior malignancy within the past 5 years except for curatively treated non-melanoma skin cancers, cervical intra-epithelial neoplasia, or localized prostate cancer with a current prostate specific antigen (PSA) of < 1.0 mg/dL Patients with other curatively treated malignancies who have no evidence of metastatic disease may be entered after discussion with the Medical Monitor.
4. Patients with known hypersensitivity to any of the components of AVN-944
5. Patients who are receiving concurrent investigational therapy or who have received investigational therapy within 14 days of the first scheduled day of dosing (investigational therapy is defined as treatment for which there is currently no regulatory authority approved indication). Clinically significant toxicities from this therapy must have resolved to < Grade 2.
6. Grade 2 peripheral neuropathy
7. Patients who are pregnant or lactating
8. Any other intercurrent medical condition, including mental illness or substance abuse, deemed by the Investigator to be likely to interfere with a patient's ability to sign the informed consent, cooperate and participate in the study, or interfere with the interpretation of the results.
9. History of solid organ transplant
10. Known HIV or hepatitis B or C (active, previously treated or both)