A woman crouches down in the doorway of a blue and yellow train at a station in Kyiv, Ukraine's embattled capital city. Her husband stands on the platform below and cranes his neck up for a kiss that both hope will not be their last.

Children look out from an evacuation train from Kyiv to Lviv as they say goodbye to their father at Kyiv central train station in central Kyiv, Ukraine, March 3, 2022.

As the train door closes, the woman holds up their 2-year-old son and he smiles and presses his tiny hand against the smudged window to wave goodbye to his father, who is staying behind to fight the Russian invaders.

Nearby, a grandmother reaches out to bid farewell to her daughter and grandson, who are on the train headed toward the border with Poland. She backs toward a wall of the train station and is soon overcome with emotion. She places her hands over her mouth, squeezes her eyes shut tight and lets the tears fall.

These are the goodbyes that have been repeated across Ukraine in the week since Russia invaded and began pounding the country's cities with bombs.

Natalia, 57, says goodbye to her daughter and grandson on a train to Lviv at the Kyiv station, Ukraine, March 3, 2022.

The United Nations says the fighting has sent more than 1 million people fleeing the country, a number that is already the swiftest exodus of refugees this century and one that could soon skyrocket even further.

Tanya, 38, cries with her son Bogdan, 10, before getting a train to Lviv at the Kyiv station, Ukraine, March 3, 2022.

Those leaving are overwhelmingly women and children. Ukrainian men have been ordered to stay and fight in the war.

A couple says goodbye before she boards a train bound for Lviv at the Kyiv station, Ukraine, March 3, 2022.

At the train station in Kyiv crowds of people carrying luggage stand in the cold as they wait for their chance to board a train. Mothers hold children bundled in winter jackets and stocking caps, some clutching onto stuffed animals.

A woman cries as she says goodbye to her husband before boarding a train bound for Lviv at the Kyiv station, Ukraine, March 3, 2022.

Men help the elderly get to the train, even using a luggage cart to carry one woman with crutches.

Up and down the platform there are tearful embraces.

A girl comforts a cat before the departure of a Lviv bound train, Kyiv, Ukraine, March 3, 2022.

Once on the train, many of those leaving press their faces against the windows for a last glimpse at those staying behind.

A girl looks out from a carriage window as a train prepares to depart from a station in Lviv, western Ukraine, en route to the town of Uzhhorod near the border with Slovakia, March 3, 2022.

One woman reaches her hand out the door for a fleeting brush of a loved one's cheek.

A woman bids a man goodbye after boarding a Lviv bound train, in Kyiv, Ukraine, March 3, 2022.

Women and children try to get onto a train bound for Lviv, at the Kyiv station in Ukraine, March 3, 2022.

Ukrainian families say goodbye as they prepare to board a bus to Poland at Lviv bus main station, western Ukraine, March 1, 2022.

A woman cries as she tries to board a free train to Poland at a train station in Lviv, western Ukraine, March 3, 2022.

A girl and her brother sit on a train bound for Lviv at the Kyiv station, Ukraine, March 3, 2022.

A woman looks toward relatives and presses her palms against a window of a Lviv bound train, on the platform in Kyiv, Ukraine, March 3, 2022.

Stanislav, 40, kisses his wife Anna, 35, on a train to Lviv as they say goodbye at the Kyiv station, Ukraine, March 3, 2022.

Women and children try to get onto a train bound for Lviv, at the Kyiv station in Ukraine, March 3. 2022.

A child clutches a man's leg before boarding a Lviv bound train, in Kyiv, Ukraine, March 3, 2022.

Women and children crowd a train bound for Lviv at the Kyiv station, Ukraine, March 3, 2022.

Bogdan, 41, says goodbye to his wife Lena, 35, on a train to Lviv at the Kyiv station, Ukraine, March 3, 2022. Bogdan is staying to fight while his family is leaving the country to seek refuge in a neighboring country.

A family runs over the tracks trying to board a Lviv bound train, in Kyiv, Ukraine, March 3, 2022.

A woman with her son looks at a train leaving as they try to flee at the Kyiv station, Ukraine, March 3, 2022.

A woman gets help after falling on the tracks trying to reach a Lviv bound train, in Kyiv, Ukraine, March 3, 2022.

Children look out the window of an unheated Lviv bound train, in Kyiv, Ukraine, March 3, 2022.

Women and children try to get onto a train bound for Lviv, at the Kyiv station in Ukraine, March 3, 2022.

A child plays with a teddy bear while waiting to board a Lviv bound train, in Kyiv, Ukraine, March 3, 2022.