Osteoarthritis (OA) of the knee: This is the most likely diagnosis given the patient's age, the nature of the pain (worsening with stairs and sudden movements), and the absence of systemic symptoms. OA is a common condition in elderly individuals, especially those with a history of diabetes and hypertension, which can affect joint health.

Meniscal tear: Sudden sharp pain, especially when stepping, could indicate a meniscal tear. This condition is common in older adults and can be exacerbated by sudden movements or twisting.
Ligament sprain: A sprain, particularly of the medial or lateral collateral ligaments, could cause knee pain that worsens with activity like going up and down stairs.
Patellofemoral pain syndrome: This condition, characterized by pain around or behind the patella, is often exacerbated by activities that put stress on the knee, like climbing stairs.

Septic arthritis: Although less likely, septic arthritis is a medical emergency that requires prompt diagnosis and treatment. The patient's history of diabetes increases her risk for infections, including septic arthritis.
Deep vein thrombosis (DVT): DVT can cause leg pain and swelling, and while it's more commonly associated with calf pain, it should be considered, especially in patients with risk factors like hypertension and diabetes.
Osteonecrosis (avascular necrosis): This condition, which can be a complication of long-term steroid use or other factors, leads to bone death due to lack of blood supply. It's a less common but serious condition that could present with sudden onset of knee pain.

Spontaneous osteonecrosis of the knee (SONK): A rare condition that typically affects older adults, characterized by sudden onset of knee pain due to a spontaneous osteonecrotic lesion.
Complex regional pain syndrome (CRPS): A rare condition characterized by intense burning or aching pain in the hands or feet after an injury or trauma. While rare, it could be considered in the differential for unexplained, severe pain.
Tumor (primary or metastatic): Although rare, a tumor in the knee could cause pain, especially if it affects the bone or surrounding tissues. Given the patient's age, metastatic disease could be a consideration, especially if there's a known primary cancer.