Diffusion capacity of the lung for carbon monoxide (DLCO) >= 40% of predicted (corrected or uncorrected for hemoglobin per institutional standards) Patients must have pulmonary function sufficient to receive bleomycin, with normal lung expansion, absence of crackles on auscultation, and normal carbon monoxide diffusion (DLCO), defined as greater than 80% predicted Documented diffusion capacity of the lung for carbon monoxide (DLCO) < 50% (if performed within 90 days of enrollment) or requirement for supplemental oxygen Pulmonary: Asymptomatic or if symptomatic, diffusion capacity of the lung for carbon monoxide (DLCO) > 50% of predicted (corrected for hemoglobin). Pulmonary function (spirometry and corrected diffusion capacity of the lung for carbon monoxide [DLCO]) >= 50% predicted. Corrected diffusion capacity of the lung for carbon monoxide (DLCOc) >= 50%; Diffusion capacity > 45% (adjusted for hemoglobin) as predicted by pulmonary function testing Within 4 weeks before enrollment: Diffusion capacity > 45% (adjusted for hemoglobin) as predicted pulmonary function testing Pulse oximetry with a baseline O2 saturation of >= 90% and diffusion capacity of the lung for carbon monoxide (DLCO) > 40% (corrected for hemoglobin) Pulmonary function tests within past 6 months showing diffusion capacity of the lung for carbon monoxide (DLCO) > 50% of predicted Pulmonary function test (PFT) demonstrating a diffusion capacity of least 50% predicted. Diffusion capacity of the lung for carbon monoxide (DLCO) > 60% Diffusion capacity of the lung for carbon monoxide (DLCO) < 40% of normal or oxygen saturation (O2 Sat) < 92% Diffusion capacity of the lungs for carbon monoxide (DLCO) (corrected for hemoglobin [Hgb]) >= 50% If measured, carbon monoxide diffusion capacity (DLCO) > 50% Other serious medical conditions considered to represent contraindications to bone marrow transplant (BMT) (e.g., abnormally decreased cardiac ejection fraction, diffusion capacity of the lung for carbon monoxide [DLCO] < 50% predicted, patient on supplemental oxygen, acquired immune deficiency syndrome [AIDS], etc.) Corrected diffusion capacity of the lung for carbon monoxide (DLCOcorr) > 50% if symptomatic or prior known impairment Adequate cardiac and pulmonary function; patients with decreased left ventricular ejection fraction (LVEF) =< 40% or diffusion capacity of carbon monoxide (DLCO) =< 50% of predicted will be evaluated by cardiology or pulmonary prior to enrollment on this protocol; patient with left ventricular assist device (LVAD) placement without heart failure symptoms will be allowed Diffusion capacity of the lung for carbon monoxide (DLCO) >= 40% predicted (corrected for hemoglobin); if unable to perform pulmonary function tests, the O2 saturation > 92% on room air Diffusion capacity of the lung for carbon monoxide (DLCO) < 40% Diffusion capacity of carbon monoxide (DLCO) < 50% predicted (corrected for hemoglobin and alveolar volume) DLCO (alveolar diffusion capacity for carbon monoxide) (corrected for hemoglobin) >= 50% of predicted Diffusion capacity of the lung for carbon monoxide (DLCO) > 60% Diffusion lung capacity of oxygen (DLCO) >= 50% of predicted corrected for hemoglobin Pulmonary function test (PFT) demonstrating a diffusion capacity of least 40% predicted Corrected diffusion capacity of the lung for carbon monoxide (DLCO) >= 50% For all patients: diffusion capacity of the lungs for carbon monoxide (DLCO) > 40% predicted (corrected for hemoglobin [Hgb]) Adequate pulmonary function with corrected diffusion capacity of carbon monoxide (DLCO) > 50% in those for whom this study can be performed Pulmonary: asymptomatic or if symptomatic, diffusion capacity of the lung for carbon monoxide (DLCO) >= 50% of predicted (corrected for hemoglobin) Corrected diffusion capacity of the lung for carbon monoxide (DLCO) >= 40% Adequate pulmonary function defined as diffusion capacity of carbon monoxide (DLCO) > 30% predicted, and absence of oxygen (O2) requirements Patients must have no significant obstructive airways disease or resting hypoxemia (partial pressure of oxygen [PO2] < 80), and must have acceptable diffusion capacity (diffusion capacity of the lung for carbon monoxide [DLCO] > 50% of predicted) Pulmonary function test and diffusion capacity of carbon monoxide (DLCO) > 50% of normal Diffusion capacity of carbon monoxide (DLCO)corr > 50% normal Diffusion capacity of oxygen, corrected for hemoglobin, > 50% of predicted Pulmonary function test (PFT) demonstrating a diffusion capacity of least 45% predicted Diffusion capacity of the lung for carbon monoxide (DLCO) > 40% with no symptomatic pulmonary disease Corrected diffusion capacity of the lung for carbon monoxide (DLCOcorr) > 50% ULN Pulmonary function (diffusion capacity of the lung for carbon monoxide [DLCO]) > 40% of the expected value corrected for alveolar volume and hemoglobin Pulmonary disease: diffusion capacity of the lung for carbon monoxide (DLCO) parameters < 60% predicted (corrected for hemoglobin) Lung diffusion capacity >= 50% Spirometry diffusion capacity (diffusion capacity of the lung for carbon monoxide [DLCO]) >= 50% Diffusion capacity of carbon monoxide (DLCO) >= 30% predicted, no oxygen (O2) requirements Other serious medical conditions considered to represent contraindications to ASCT (e.g., abnormally decreased cardiac ejection fraction, diffusion capacity of the lung for carbon monoxide [DLCO] < 50% predicted, acquired immune deficiency syndrome [AIDS], etc.) Patients with a diffusion capacity of the lung for carbon monoxide (DLCO) < 50% of normal or Corrected diffusion capacity of the lung for carbon monoxide (DLCO) > 45% of expected value Respiratory compromise, defined as ventilation tests with diffusion capacity of the lung for carbon monoxide (DLCO) < 50% Idiopathic interstitial pneumonia or impaired diffusion capacity of the lung for carbon monoxide (DLCO). Other serious medical conditions considered to represent contraindications to ASCT (e.g., abnormally decreased cardiac ejection fraction, diffusion capacity of carbon monoxide [DLCO] < 50% predicted, etc.) Pulmonary diffusion capacity > 25% lower than normal predicted value Patients with significant, symptomatic deterioration of lung function confirmed by spirometry, diffusion capacity of the lungs for carbon monoxide (DLCO), or resting oxygen (O2) saturation Corrected pulmonary diffusion capacity of greater than or equal to 50% Adequate pulmonary function as assessed by diffusion capacity of the lung for carbon monoxide (DLCO) of >= 45% adjusted for hemoglobin Subjects with asymptomatic pulmonary function based on lung diffusion testing diffusion capacity of the lung for carbon monoxide (DLCO) test; DLCO >= 50% of predicted (corrected for hemoglobin) Diffusion capacity of the lung for carbon monoxide (DLCO) >= 30% predicted within 6 weeks prior to study enrollment; no oxygen (O2) requirements Pulmonary: asymptomatic or if symptomatic, diffusion lung capacity of carbon monoxide (DLCO) > 40% of predicted (corrected for hemoglobin) Diffusion lung capacity of carbon monoxide (DLCO) < 40% predicted Corrected diffusion lung capacity of carbon monoxide (DLCO) < 35% or receiving supplemental continuous oxygen Pulmonary: asymptomatic or if symptomatic, diffusion capacity of carbon monoxide (DLCO) > 50% of predicted (corrected for hemoglobin) Subjects with clinical signs of pulmonary insufficiency must have diffusion capacity of the lung for carbon monoxide (DLCO) to be measured at >= 50% of predicted value Patients with active pulmonary infection and/or pulse oximetry < 90% and a corrected diffusion capacity of the lung for carbon monoxide (DLCO) < 70% of predicted Corrected diffusion capacity of carbon monoxide (DLCO) < 35% and/or receiving supplemental continuous oxygen Diffusion capacity of the lung for carbon monoxide (DLCO) > 50% of the expected value when corrected for hemoglobin (Hb), obtained within 28 days of enrollment Pulmonary function tests as follows: diffusion capacity of the lungs for carbon monoxide (DLCO) > 50% predicted Corrected diffusion capacity of the lung for carbon monoxide (DLCO) equal or above 50% of expected Subjects > 10 years: DLCO (diffusion capacity) > 50% of predicted (corrected for hemoglobin) Pulmonary function test (PFT) demonstrating a diffusion capacity of least 50% predicted, corrected for hemoglobin Diffusion capacity of the lung for carbon monoxide (DLCO) < 30% predicted (post-bronchodilator) Patients with prior smoking history or emphysema will require diffusion lung capacity for carbon monoxide (DLCO) of >= 80% of predicted value for age Diffusion capacity of carbon monoxide (DLco) <50% of predicted (corrected for hemoglobin). Adjusted diffusion capacity of the lung for carbon monoxide (DLCO) < 60% Meeting institutional criteria for allo-HCT; ejection fraction by echocardiogram or multi-gated acquisition scan (MUGA) > 40%, pulmonary function test with adjusted diffusion capacity of the lung for carbon monoxide (DLCO) >= 60% Corrected diffusion capacity of the lung for carbon monoxide (DLCO) >= 50% by pulmonary function test